Fraction Sentence Examples

fraction
  • His expression was bewildered for only a fraction of a second, and then he made a face.

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  • A known fraction of the current is then indicated and measured.

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  • I'm sure prices were a fraction of today.

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  • The thirty-four extant are but a small fraction.

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  • They say another fraction of an inch, or another five minutes.

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  • Destiny looked surprised for a fraction of a second before she started to scream.

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  • We thus express P=Q in the form of a continued fraction, k+ + I, which is usually written,for conciseness, k+ s + t + &c., s t+&c.

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  • For the dark rings Ji(z) =o; so that the fraction of illumination outside any dark ring is simply Jo 2 (z).

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  • When we know the mass of the earth in gravitational measure, its product by the denominator of the fraction just mentioned gives the mass of the sun in gravitational measure.

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  • In general, we may say that aberration is unimportant when it nowhere (or at any rate over a relatively small area only) exceeds a small fraction of the wavelength (X).

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  • The position of the middle of the bright band representative of a mathematical line can be fixed with a spider-line micrometer within a small fraction of the width of the band, just as the accuracy of astronomical observations far transcends the separating power of the instrument.

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  • A fraction of a second later the aperture occupies a bright place, and the star reappears.

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  • The works of the Arabian medical writers who have now been mentioned form a very small fraction of the existing literature.

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  • He was also the first to consider the difficult problems involved in equations of mixed differences, and to prove that an equation in finite differences of the first degree and the second order might always be converted into a continued fraction.

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  • Fleuss consists of a vacuum pump capable of reducing the air pressure to a fraction of a millimetre, the suction pipe of which is connected first with a vessel containing sulphuric acid, and second with the vessel containing the water to be frozen.

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  • Many of these items may be just like new but cost a fraction of the original price.

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  • It may differ even by a considerable fraction of a second..

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  • The larger the bridge, the more important is economy of material, not only because the total expenditure is more serious, but because as the span increases the dead weight of the structure becomes a greater fraction of the whole load to be supported.

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  • The theory, however, starts with the publication in 16J5 by Lord Brouncker of the continued fraction I 23252 i 2 + 2 + 2 +.

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  • Its amount varies a fraction of a minute for the same date, from year to year and from one longitude to another, on the same day.

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  • She wore a tee shirt with no bra, perhaps in some vague attempt to emulate Penny, but with only a fraction of the appropriate equipment.

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  • He lifted his micro, which pulsed red for a fraction of a moment.

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  • This ingenious operation widens the track at the expense of an unimportant fraction of its length.

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  • We cannot, for instance, say that the fraction C _2 I is arithmetically equal to x+I when x= I, as well as for other values of x; but we can say that the limit of the ratio of x 2 - I to x - I when x becomes indefinitely nearly equal to I is the same as the limit of x+ On the other hand, if f(y) has a definite and finite value for y = x, it must not be supposed that this is necessarily the same as the limit which f (y) approaches when y approaches the value x, though this is the case with the functions with which we are usually concerned.

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  • As the sinking of shafts or the driving of narrow entries or drifts is expensive, and as the mineral extracted rarely pays more than a small fraction of the cost, it is usual to plan this exploratory work so that the openings made shall serve some useful purpose later.

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  • After he had minutely arranged the Eastern Detachment in a series of rearguard positions, so that each fraction of it could contribute a little to the game of delaying the enemy before retiring on the positions next in rear, the commander of the detachment, Zasulich, told him that " it was not the custom of a knight of the order of St George to retreat," and Kuropatkin did not use his authority to recall the general, who, whether competent or not, obviously misunderstood his mission.

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  • The one piastre piece is worth a fraction over 24d.

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  • The toluene fraction requires a more thorough washing with sulphuric acid in order to eliminate the thiotolene, which is sulphonated much less readily than thiophene.

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  • It dissolves in a fraction of its weight of even cold water, forming a syrupy solution.

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  • An order in council was enacted in 1899 providing that no Maltese (except students of theology) should thenceforth suffer any detriment through inability to pass examinations in Italian, in either the schools or university, but the fraction of the Maltese who claim to speak Italian (13.24%) still command sufficient influence to hamper the full enjoyment of this emancipation by the majority.

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  • After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

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  • We can thus measure as described the drop in volts down a known fraction of the whole high resistance and therefore calculate the fall in potential down the whole of the high resistance, which is the potential difference required.

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  • The time since the last glacial epoch is but a fraction of the time since the first probably no more than a fifteenth or a twentieth.

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  • The general test of irrationality which he established is that, if a l a, a, be an interminate continued fraction, a l, a2,

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  • Now, As The Year Consists Of 365 Days And A Fraction, And 365 Is A Number Not Divisible By 12, It Is Impossible That The Months Can All Be Of The Same Length And At The Same Time Include All The Days Of The Year.

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  • This Differed From The Solar Year By Ten Whole Days And A Fraction; But, To Restore The Coincidence, Numa Ordered An Additional Or Intercalary Month To Be Inserted Every Second Year Between The 23Rd And 24Th Of February, Consisting Of Twenty Two And Twenty Three Days Alternately, So That Four Years Contained 1465 Days, And The Mean Length Of The Year Was Consequently 3664 Days.

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  • Now, From The Manner In Which The Intercalation Is Directed To Be Made (Namely, Seven Times Successively At The End Of 300 Years, And Once At The End Of 400), It Is Evident That The Fraction 2 Must Amount To Unity When The 5 Number Of Centuries Amounts To Twenty Four.

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  • The change of frequency (dn) for a series of lines which behave similarly is approximately proportional to the frequency (n) so that we can take the fraction do/n as a measure of the shift.

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  • The first question he answered from his imagination by supposing that, while the external world is stimulus of the nervous process, the nervous process is the immediate stimulus of the sensation, and that the sensation increases by a constant fraction of the previous stimulus in the nervous system, when Weber's law proves only that it increases by a constant fraction of the previous stimulus in the external world.

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  • The spread of toleration, which always savours minorities, broke down between 1845 and 1873 the Lutheran exclusiveness of Norway, Denmark and Sweden; but as yet the Catholics form a disappearing fraction of the population.

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  • Pennsylvania is by far the most important coalproducing state in the Union, and as much of the iron ore of the Lake Superior region is brought to its great bituminous coal-field for rendering into pig-iron, the value of the state's mineral products constitutes a large fraction of the total value for the entire country; in 1907, when the value of the mineral products of the state was $ 6 57,7 8 3,345, or nearly one-third that of all the United States, and in 1908 when the total for the state was $473,083,212, or more than one-fourth that of the whole United States, more than fourfifths of it was represented by coal and pig-iron.

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  • In this case the carbonaceous beds-coal-seams-naturally appealed most strongly to the imagination, and the name is a good one, notwithstanding the fact that coal-seams occupy but a small fraction of the total thickness of the Carboniferous system; and although subsequent investigations have demonstrated the existence of coal in other geological formations, in none of these does it play so prominent a part.

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  • Curie obtained only a fraction of a gramme of the chloride and Giesel 2 to 3 gramme of the bromide from a ton of uranium residues.

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  • If this arrangement is expressed by a fraction, the numerator of which indicates the number of turns, and the denominator the number of internodes in the spiral cycle, the fraction will be found to represent the angle of divergence of the consecutive leaves on the axis.

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  • In this simple case the temperature cycle at a depth x is a precisely similar curve of the same period, but with the amplitude reduced in the proportion rn ', and the phase retarded by the fraction mx/27r of a cycle.

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  • The motor field, therefore, though absolutely larger, forms a smaller fraction of the whole cortex of the brain than in the lower forms. The statement that in the anthropoid (orang-outan) brain the groups of foci in the motor fields of the cortex are themselves separated one from another by surrounding inexcitable cortex, has been made and was one of great interest, but has not been confirmed by subsequent observat'on.

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  • Yet it is but a small fraction of the ulema of the Moslem world that enjoy even such an education as the Azhar affords.

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  • We may therefore conclude that for large classes of characters, both animal and vegetable, the variability of an individual, as measured by the standard deviation of its undifferentiated but repeated organs, is a constant fraction of the variability of its race, as measured by the standard deviation of the corresponding series of organs produced by all the individuals of its race.

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  • They are subjected to incredible abuses under Spanish colonial rule, their numbers being reduced to a fraction of the former population, and even yet they are subjected to a kind of debt-bondage which is slavery in all but the name.

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  • Only a small fraction of Goethe's work was written in an impersonal and objective spirit, and sprang from what might be called a conscious artistic impulse; by far the larger - and the better - part is the immediate reflex of his feelings and experiences.

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  • Recent research in bringing to light considerable portions of long-forgotten ages is revolutionizing those impressions which were based upon the Old Testament - the sacred writings of a small fraction of this.

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  • The executive of 5 members and the legislature or Landrat (one member per Boo inhabitants or fraction over 400), as well as the single member sent to the Federal Steinderat and the three sent to the Federal Nationalrat, are all elected by a direct popular vote for three years.

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  • The Landsgemeinde is the supreme legislative authority, and elects both the executive (in Inner Rhoden composed of nine members and called Stdndeskommission, and in Ausser Rhoden of seven members and called Regierungsrath) and the president or Landammann; in each half-canton there is also a sort of standing committee (composed of the members of the executive and representatives from the communes - in Inner Rhoden one member per 250 or fraction over 125 of the population, and in Ausser Rhoden one member per 1000 of the inhabitants) which prepares business for the Landsgemeinde and decides minor matters; in Inner Rhoden it is named the Grossrath and in Ausser Rhoden the Kantonsrath.

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  • This is a tall iron erection, built up from superposed cylinders, which are separated from one another by perforated horizontal diaphragms, con this recovery is carried out in the most efficient manner, the process cannot possibly pay; but so much progress has been made in this direction that the loss of ammonia is very slight indeed, merely a fraction per cent.

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  • The inland transit of goods is almost entirely on the backs of bulls carrying from 450 to 600 lb, on ponies carrying 200 ib, and on men carrying from l00 to 150 lb, bringing the average cost up to a fraction over 8d.

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  • The exact determination of the appearances in any given case is a mere problem of convergents to a continued fraction.

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  • Such are but a fraction of its achievements.

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  • We learn that if the orbital motion of a planet, or a satellite, were arrested, the body would fall into the sun, or into its primary, in the fraction 0.1768 of its actual periodic time.

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  • The usual empirical assumption is that u21ui= e(ufui), (41) where e is a proper fraction which is constant for the same two bodies.

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  • But neither this nor the diminution of the marriagerate amongst women of those ages suffices to account for more than a fraction of the decline.

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  • Marriage and child-bearing, in the first place, are operative amongst a fraction of the population only - those of conceptive age; whereas to the Urn of Death, as Dr Farr expressed it, all ages are called upon to contribute in their differing degrees.

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  • They form, however, but a small fraction of the entire production of the country.

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  • He found that a small fraction, not more thanoth part, resisted the change, and in this residue he doubtless had a sample of the inert gas argon which was only recognized as a distinct entity more than a hundred years later.

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  • The subject was pursued by Thomson and the Cambridge physicists with great mathematical and experimental ability, and finally the conclusion was reached that in a high vacuum tube the electric charge is carried by particles which have a mass only a fraction, as above mentioned, of that of the hydrogen atom, but which carry a charge equal to the unit electric charge of the hydrogen ion as found by electrochemical researches.

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  • In the same way it may be employed to measure high potentials by measuring the fall of potential down a fraction of a known non-inductive resistance.

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  • The membership of the lower house is in the proportion of one deputy for each 30,000 of the departmental population, and each fraction over 15,000; and the senate is entitled to one-third the membership of the chamber.

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  • If the continued fraction terminates, it is said to be a terminating continued fraction; if the number of the quantities a, ..., b 2 ..

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  • If b 2 /a 2, 3 /a 3 ..., the component fractions, as they are called, recur, either from the commencement or from some fixed term, the continued fraction is said to be recurring or periodic. It is obvious that every terminating continued fraction reduces to a commensurable number.

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  • The notation employed by English writers for the general continued fraction is al b2 b3 b4 a 2 "' Continental writers frequently use the notation a 1 ?

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  • In the case of the fraction a 1 - a2 _ a3 _a4 _ we have the relations p n = = ang n-1 - bngn-2 Taking the quantities a l..

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  • It is evident that, in this case, P ' p2, are two series of positive integers increasing without limit if the fraction does not terminate.

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  • The general continued fraction al is evidently equal, convergent by convergent, to the continued fraction X 2 b 2 X2X3b3 x3%4b4 a1+ A2a2 + X + X

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  • The simple continued fraction is both the most interesting and important kind of continued fraction.

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  • Any quantity, commensurable or incommensurable, can be expressed uniquely as a simple continued fraction, terminating in the case of a commensurable quantity, non-terminating in the case of an incommensurable quantity.

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  • A non-terminating simple continued fraction must be incommensurable.

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  • In the case of a terminating simple continued fraction the number of partial quotients may be odd or even as we please by writing the I last partial quotient, a n as a n - I +1.

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  • Every convergent is nearer to the value of the whole fraction than any preceding convergent.

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  • Every convergent is a nearer approximation to the value of the whole fraction than any fraction whose denominator is less than that of the convergent.

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  • The difference between the continued fraction and the nth convergent is less than, and greater than a n+2 These limits qn may be replaced by the following, which, though not so close, are simpler, viz.

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  • Every simple continued fraction must converge to a definite limit; for its value lies between that of the first and second convergents and, since f ?n _ _1 I, L t.

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  • The chief practical use of the simple continued fraction is that by means of it we can obtain rational fractions which approximate to any quantity, and we can also estimate the error of our b4 as a4 b5 approximation.

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  • Thus a continued fraction equivalent to 7r (the ratio of the circumference to the diameter of a circle) is I I I I II 3+ 7+15+7+292+i-1-i+ ..

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  • Similarly the continued fraction given by Euler as equivalent to 1(e - 1) (e being the base of Napierian logarithms), viz.

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  • If we suppose alb to be converted into a continued fraction and p/q to be the penultimate convergent, we have aq-bp= +1 or -1, according as the number of convergents is even or odd, which we can take them to be as we please.

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  • The value of such a fraction is the positive root of a quadratic equation whose coefficients are real and of which one root is negative.

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  • Since the fraction is infinite it cannot be commensurable and therefore its value is a quadratic surd number.

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  • Conversely every positive quadratic surd number, when expressed as a simple continued fraction, will give rise to a recurring fraction.

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  • The second case illustrates a feature of the recurring continued fraction which represents a complete quadratic surd.

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  • In the case of a recurring continued fraction which represents N, where N is an integer, if n is the number of partial quotients in the recurring cycle, and pnr/gnr the nr th convergent, then p 2 nr - Ng2nr = (- I) nr, whence, if n is odd, integral solutions of the indeterminate equation x 2 - Ny 2 = I (the so-called Pellian equation) can be found.

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  • The theory and development of the simple recurring continued fraction is due to Lagrange.

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  • It is always possible to find the value of the n th convergent to a recurring continued fraction.

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  • Let the fraction be a l a 2 al +...

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  • We have seen that the simple infinite continued fraction converges.

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  • The infinite general continued fraction of the first class cannot diverge for its value lies between that of its first two convergents.

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  • The infinite continued fraction a2 +a3+ an ..

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  • A continued fraction may always be found whose n th convergent shall be equal to the sum to n terms of a given series or the product to n factors of a given continued product.

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  • If we form then the continued fraction inwhich pi, p2, p3 9 ..., pn are u1, u1 + u 2, ul+u2+u3,

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  • In this case the sum to n terms of the series is equal to the nth convergent of the fraction.

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  • There is, however, a different way in which a series may be represented by a continued fraction.

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  • Here the fraction converges to the sum to infinity of the series.

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  • Lambert for expressing as a continued fraction of the preceding type the quotient of two convergent power series.

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  • There is another type of continued fraction called the ascending continued fraction, the type so far discussed being called the descending continued fraction.

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  • The notation for this type of fraction is b4 + b5+ b3+ al b2 + a4 a3 It is obviously equal to the series b 2 b3 b4 b5 al +a 2 +aza3a4 + a2a3a4a 5 + .

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  • John Wallis, discussing this fraction in his Arithmetica finitorum (1656), gives many of the elementary properties of the convergents to the general continued fraction, including the rule for their formation.

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  • Huygens (Descriptio automati planetarii, 1703) uses the simple continued fraction for the purpose of approximation when designing the toothed wheels of his Planetarium.

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  • In the case of sea-fishes it is becoming increasingly recognized that the millions of cod fry which are annually turned out of the American, Newfoundland and Norwegian hatcheries are but an insignificant fraction of the billions of fry which are naturally produced.

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  • No change in the capillary conditions can arise until the interval is reduced to a small fraction of a wave-length of light; but such a reduction, unless extremely local, is strongly opposed by the remaining air.

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  • It would seem that the surfaces, coming into collision within a fraction of a second of their birth, would still be subject to further contamination from the interior.

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  • Under modern conditions there is little danger from such a dissemination of the forces, as each fraction of each army corps is within less than two hours' march of its concentration post.

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  • He has been styled the "bishop of society"; but society occupied only a fraction of his time.

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  • The amount of pyridine produced in most of these processes is very small, and the best source for its preparation is the "light-oil" fraction of the coal-tar distillate.

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  • The story of the pagan past slipped out of mind, and in its place was set, by the genius of Eusebius, the story of the world force which had superseded it, Christianity, and of that small fraction of antiquity from which it sprang, - the Jews.

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  • But even these vast sets cover but the merest fraction of their subjects.

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  • The Mestizos, who form so large a fraction of the population of modern Mexico, numbering several millions, afford a convenient test in this respect, inasmuch as their intermediate complexion separates them from both their ancestral races, the Spaniard, and the chocolate-brown indigenous Aztec or other Mexican.

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  • By an amendment of 1900, the legislature was instructed to provide that a fixed fraction of the voters might cause any law to be submitted to the people, or that they might require any legislative act (except one passed by a two-thirds vote of each house) to be so submitted before going into effect, but up to 1910 no law had been passed putting the amendment into force.

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  • For his personal use, however, he retained but a very small fraction of the sums thus acquired, and at his death his private fortune amounted to scarce a million florins.

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  • The fraction of the incident radiation which is not absorbed by a body gives a measure of its reflecting power, with which we are not here concerned.

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  • If lo represents the intensity of the light which enters the surface, I l the intensity after passing through i centimetre, I 2 the intensity after passing through 2 centimetres, and so on; then we should expect that whatever fraction of Io is absorbed in the first centimetre, the same fraction of I, will be absorbed in the second.

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  • The energy which the sun pours out into space is, so far as we know, and except for the minute fraction intercepted by the disks of the planets (ii?oooo") absolutely lost for the pur.

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  • Thus the benefit to the fisheries and to the riparian owners generally is beyond all question; but the cost to the water authority of conferring that benefit is also very great - commonly (according to the proportion of the natural flow intended to be rendered uniform) 20 to 35% of ' The volume of compensation water is usually fixed as a given fraction of the so-called " available supply " (which by a convention that has served its purpose well, is understood to be the average flow of the stream during the three consecutive driest years).

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  • In conformity with the above-mentioned convention (by which compensation water is determined as a certain fraction of the average flow during the three driest consecutive years) the available supply or flow from a given area is still understood to be the average annual rainfall during those years, less the corresponding evaporation and absorption by vegetation.

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  • The average volume in dry weather, of such flow, generally reduced to terms of the fraction of a cubic foot per second, per thousand acres of the contributing area, is commonly known in water engineering as the " dry weather flow " and its volume at the end of the dry season as the " extreme dry weather flow."

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  • It would conceivably take but a small fraction of the period that has in most cases elapsed since such upheavals occurred for the salt water to be thus displaced by fresh water, and for the condition to be attained as regards saturation with fresh water, in which with few exceptions we now find the porous portions of the earth's crust wherever the rainfall exceeds the evaporation.

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  • A fraction of a quantity is a submultiple, or a multiple of a submultiple, of that quantity.

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  • Hence the value of a fraction is not altered by substituting for the numerator and denominator the corresponding numbers in any other column of a multiple-table (§ 36).

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  • If we write 74 in the form 47 we may say that the value of a fraction is not altered by multiplying or dividing the numerator and denominator by any number.

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  • Fraction of a Fraction.-To find of 7 of A we must convert 7 of A into 4 times some unit.

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  • A fractional number is called a proper fraction or an improper fraction according as the numerator is or is not 3 less than the denominator; and an expression 4 such as 24 is called a mixed number.

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  • An im 5 proper fraction is therefore equal either to an 2 I integer or to a mixed number.

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  • The rule for multiplying a fractional number by a fractional number is therefore the same as the rule for finding a fraction of a fraction.

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  • The idea and properties of a fractional number having been explained, we may now call it, for brevity, a fraction.

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  • Thus "-4 of A " no longer means two of the units, three of which make up A; it means that A is multiplied by the fraction 3, i.e.

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  • If the numerator is a multiple of 5, the fraction represents twentieths.

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  • A fraction written in this way is called a decimal fraction; or we might define a decimal fraction as a fraction having a power of To for its denominator, there being a special notation for writing such fractions.

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  • His eyes flashed for a fraction of a second, and then all emotion was removed from them.

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  • I can't remember the time before the Schism, except for you and Darian, and my magic is but a fraction of what it once was.

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  • How would a human who lived a fraction of one life judge my actions as foolish?

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  • Now that she possessed a fraction of the Dark One's power, she would heal instantly.

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  • Surely if it be blessed with even a fraction of the goodness and kindness of its father, the child deserves all the blessings of life; far more than might be offered by this wretch of a woman God may deem to mother it into the world.

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  • Whatever they paid this super cop, it wasn't a fraction of his worth when it came to effec­tive PR.

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  • In fact, you can find specialized outfits at many department stores for a fraction of what you would have to pay at a specialty shop.

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  • A mixed number, the fractional part of which is a decimal fraction, is expressed by writing the integral part in front of the point, which is called the decimal point.

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  • This number, expressed in terms of the fraction ioo, T oor 0001, would be 271530.

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  • The only known exception was the use of * as a single fraction.

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  • Except in the case of - and 2, the fraction was expressed by the denominator, with a special symbol above it.

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  • The Babylonians expressed numbers less than r by the numerator of a fraction with denominator 60; the numerator only being written.

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  • The pth root of a number (§43) may, if the number is an integer, be found by expressing it in terms of its prime factors; or, if it is not an integer, by expressing it as a fraction in its lowest terms, and finding the pth roots of the numerator and of the denominator separately.

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  • For multiplication by a proper fraction or a decimal, it is sometimes convenient, especially when we are dealing with mixed quantities, to convert the multiplier into the sum or difference of a number of fractions, each of which has i as its numerator.

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  • Division by a Mixed Number.-To divide by a mixed number, when the quotient is seen to be large, it usually saves time to express the divisor as either a simple fraction or a decimal of a unit of one of the denominations.

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  • If the denominator of the fraction, when it is in its lowest terms, contains any other prime factors than 2 and 5, it cannot be expressed exactly as a decimal; but after a certain point a definite series of figures will constantly recur.

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  • A continued fraction, of the kind we are considering, is an expression of the form a+ b+ c + d+ &c.

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  • Any exact fraction can be expressed as a continued fraction, and there are methods for expressing as continued fractions certain other numbers, e.g.

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  • A considerable fraction of them adhered consistently to the English cause from this time forth, and ultimately lost their lands for refusing to follow the rest of the nation in the next insurrection.

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  • Analytical investigations revealed the existence of series or sequences which had no limit to the number of terms, as for example the fraction 1/(1 - x) which on division gives the series.

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  • The National Assembly is a single chamber, whose deputies (each at least 25 years old) are elected for four years by popular vote on the basis of 1 to every 10,000 inhabitants (or fraction over 5000); it meets biennially; by a two-thirds vote it may pass any bill over the president's veto - the president has five or ten days, according to the length of the bill, in which to veto any act of the legislature.

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  • Although Royalists formed but a petty fraction of the majority, they raised the alarm that Mth i t w as seeking to restore monarchy and undo the work of the /8th g y of the Revolution.

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  • These suggestions took practical shape by a decree of the National Assembly in 1790 appointing a committee to consider the suitability of adopting either the length of the seconds pendulum, a fraction of the length of the equator or a fraction of the quadrant of the terrestrial meridian..

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  • Kepler's third law therefore expresses the fact that the mass of the sun is the same for all the planets, and deviates from the truth only to the extent that the masses of the latter differ from each other by quantities which are only a small fraction of the mass of the sun.

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  • Not the slightest change in the direction of such a star when in this position has ever been detected, and it is certain that if any occurs it can be but a minute fraction of a second of arc. As an atmosphere equal to ours in density would produce a deviation of an important fraction of a degree, it may be said that the moon can have no atmosphere exceeding in density the b b l o o that of the earth.

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  • The actual duties of the office were in such cases carried out by ordained and older men for a fraction of the stipend.

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  • They also investigated certain hydrocarbons occurring in the high boiling point fraction of the coal tar distillate and solved the constitution of phenanthrene.

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  • There was no native coinage, the French 5-franc piece or dollar being the standard, and all sums under that amount were obtained by cutting up those coins into all shapes and sizes, which were weighed with small weights and scales into halves, quarters, eighths, twelfths and twenty-fourths of a dollar, and even reckoned down to the seven hundred and twentieth fraction of the same amount.

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  • To an outsider it also appears that the staff of officials is very largely in excess of any real needs of administration; several monopolies, which interfere with the habits of the people, tend to produce discontent; and the taking of their land and houses for public works, roads, &c., while but a mere fraction of their real value is allowed as compensation, does not help to increase their acquiescence in foreign control.

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  • The Peltier effect was only a small fraction of the total effect, but could be separated from the Joule effect owing to the reversal of the current.

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  • All except a small fraction of the copper ore is obtained from the province of Huelva, in which lie the well-known mines of Tharsis and Rio Tinto (q.v).

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  • It enabled the honey producer to increase his output considerably by extracting honey from the cells in most cleanly fashion without damaging the combs, and in a fraction of the time previously occupied in the draining, heating and squeezing process.

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  • Corresponding to the size of the yellow spot only a small fraction of the image appears particularly distinctly.

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  • With this mineral also spherical and chromatic aberration are a fraction of that of a glass lens, but double refraction, which involves a doubling of the image, is fatal to its use.

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  • Then the denominator of the fraction, the numerical aperture, must be correspondingly increased, in order to ascertain the real resolving power.

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  • Currents from the ten-thousandth of an ampere to ten thousand amperes, electrical pressures from a minute fraction of a volt to 100,000 volts, come within the range of his instruments, while the private consumer of electric energy is provided with a meter recording Board of Trade units.

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  • The name Fraticelli may more justly be applied to the most exalted fraction of Franciscanism.

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  • It is this fraction of the order which John XXII.

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  • It required only a fraction of a second to be reminded that her original career goal would never be achieved.

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  • The trees rustled as he dispelled a fraction of his power.

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  • She saw the wounded look a fraction of a moment before the Black God hardened.

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  • She hesitated then said slowly, "If you felt a fraction of what I did in the wine cellar …" "Good," he said.

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  • A significant fraction of the oxy radical also reacts via hydrogen atom abstraction from the added reagent.

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  • The condenser aperture controls the fraction of the beam which is allowed to hit the specimen.

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  • The fact is you CAN obtain a barony for a fraction of what these colluding companies demand of you in payment.

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  • With the density of baryonic matter known, the total density can be determined from measuring the baryon fraction.

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  • Only a fraction of it has to melt to trigger a cataclysm.

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  • The milk was separated by centrifugation into the cell fraction at the bottom, fat at the top and solution in between.

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  • The mitotic index is the fraction of cells in a microscope field which contain condensed chromosomes.

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  • The use of creatine is now commonplace, with supplements widely available at a fraction of the original cost.

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  • Only a fraction of our total brain capacity is dedicated to verbal communication.

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  • This is because MPEG digitally compresses signals down to a fraction of their bandwidth size.

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  • Therefore, only a small fraction of the total energy out put from solar is required to heat the corona.

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  • If even a fraction of these reports were true, there would now be a great dearth of foxes in our cities.

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  • Each listed inch fraction has the smallest denominator that keeps the value within the ISO 216 tolerance limits.

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  • She counted out lots corresponding to the posited fraction denominator.

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  • Equipment is available at a fraction of the cost of hiring a Private detective which can give you all the evidence that you need!

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  • Read Math Spoken Here, featuring the essays " Most Operations Are not distributive, " " So, What's A Fraction?

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  • The pulse duration of a wide pulse, on the other hand, is a large fraction of the period of the waveform.

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  • The radiation emitted from a cluster comes from a very small fraction of the mass present.

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  • The NPL low drift etalon has extremely low overshoot and settles in a fraction of the time of conventional etalons.

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  • The precision value specifies the number of fraction digits in the result. | Pops three values and computes a modular exponentiation.

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  • However, these represent a fraction of the total number of deaths.

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  • Deaths from ecstasy in Holland are only a tiny fraction of the figures for Britain.

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  • In the example you quote £ 10.31 the " .31 " is a decimal fraction of a pound, not of the pence.

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  • The mean left ejection fraction was 69 %, and 31% had a left ejection fraction above 40% .

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  • Similarly, the mole fraction of ethanol is 1/3.

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  • Certainly, modification of the lipid fraction is important, but so is co-ordination of cellular activity.

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  • A small fraction of that amount could fully commercialize fuel cells within five years and create tens of thousands of jobs.

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  • The allergenic fraction of bee glue is found in the volatile oil derived from it by distillation.

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  • Now you can have the " most expensive hamburger " at home, for a fraction of the price.

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  • In periventricular heterotopias, a fraction of the post-mitotic neurones are incapable of leaving the ventricular zone.

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  • Well, like the proverbial iceberg, what you see on the surface is only a fraction of what exists.

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  • The old explanations seem either implausible, or they explain only a fraction of cases.

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  • The all action Bowyer managed to work an opening, but saw his 20 yard lob clear the bar by a fraction.

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  • If it begins to feel dead, ease the mainsheet a fraction.

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  • The SI base unit for concentration is the mol, from which atom fraction and mol fraction are derived.

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  • We have also only included coins which contain a simple fraction of a troy ounce of gold.

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  • Delicious home-made pizzas put most fancy Italian sit down joints to shame, at a fraction of the price.

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  • It might also be a fraction too early to discuss the ramifications of romantic developments.

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  • A burst of gamma rays from space lasting from a fraction of a second to many minutes.

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  • Daniel had the grace to look shamefaced - for a fraction of a second.

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  • But now, you can produce stunning, full-colour labels for a fraction of the cost of other color label printers.

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  • Depth of the anterior chamber at the temporal limbus was graded as a percentage fraction of peripheral corneal thickness.

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  • Furthermore current technology has purification procedures for only a fraction of known plant toxicants.

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  • A narrow gage tramway would take up a fraction of the space needed for the CDTS scheme.

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  • Cheaper turmeric products simply use culinary turmeric products simply use culinary turmeric which contains only a fraction of the curcumin.

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  • In beef cows, who have small udders, the incidence of mastitis is a fraction of that in dairy herds (29 ).

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  • D is the drum-head which gives the fraction of a revolution, d that which gives the whole number of revolutions, I is the index or pointer at which both drums are read.

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  • Under such powers the webs can be brought into apparent contact with such precision and delicacy that the uncertainty of measurement seems to lie as much in the estimation of the fraction of the division of the head as in the accuracy of the contact.

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  • This comb does not move with reference to the box, and serves to indicate the whole revolution of which a fraction is read on the head.

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  • To be a fraction of the corporate sovereign, if it had its gains, had also its disadvantages; the Venetian noble was fettered by burthens, restrictions and suspicions from which the Venetian citizen was free.

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  • The average acceleration in feet per second is measured by the fraction Change of speed in feet per sec. 60.07-58.6 64 tons; and to obtain the horse-power the boiler will be one of the largest that can be built to the construction gauge.

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  • No contemporary, unaided by personal knowledge, could be expected to trust in Wagner's purity of ideal on the strength of Tannhauser, which actually achieved popularity by such coarse methods of climax as the revivalistic end of the overture, by such maudlin pathos as 0 du mein holder Abendstern, and by the amiably childish grand-opera skill with which half the action is achieved by processions and a considerable fraction of the music is represented by fanfares.

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  • For the subjects of this general heading see the articles ALGEBRA; ALGEBRAIC FORMS; ARITHMETIC; COMBINATORIAL ANALYSIS; DETERMINANTS; EQUATION; FRACTION, CONTINUED; INTERPOLATION; LOGARITHMS; MAGIC SQUARE; PROBABILITY.

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  • There is therefore in a large class, of cases an indication that the variability of an array of brethren, produced either sexually or asexually, is a constant fraction of the variability of the race to which the brethren belong.

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  • For the convergence of the continued fraction of the second class there is no complete criterion.

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  • The hydrocarbon occurs in wood-tar and in petroleum, and is prepared commercially by fractional distillation of the light oil fraction of the coal-tar distillate (see Coal Tar).

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  • Open pyre burning could handle only a fraction of the balance, not least because it soon attracted a considerable public outcry.

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  • This is the reciprocal of the fraction let through and is usually given in decibels.

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  • The fact is that there are so many rotting hulks out there and the number of restorations is a minute fraction of the total.

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  • Accurate segmentation can be achieved in a fraction of the time it would take to trace the boundary by hand.

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  • This is my Root Rational Fraction program, which does exact arithmetic on quantities that are square roots of rational fractions.

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  • Beryllium, unfortunately, is a toxic material, and increasing the Be fraction in the recipe actually depressed the superconductivity transition temperature.

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  • We, as your ISP, receive a fraction of the amount that you pay to your telecom 's provider on the 0844 number.

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  • Cheaper turmeric products simply use culinary turmeric which contains only a fraction of the curcumin.

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  • In beef cows, who have small udders, the incidence of mastitis is a fraction of that in dairy herds (29).

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  • You can often find great deals at a fraction of the cost of a new item!

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  • Wipes-There are many store brand baby wipes that work just as well as name brand ones, but at a fraction of the cost.

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  • Consignment Shops-These shops sell used clothing for a fraction of the cost.

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  • The good news is that you can find great, used items at a fraction of the price you'd normally pay.

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  • You can stock up on baby gift items, supplies, and clothing for the next year at a fraction of the cost of what you would normally pay.

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  • Online auction companies, such as eBay allow people to sell their preemie clothing for often a fraction of the original price.

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  • Because premature babies will outgrow their clothing pretty quickly, you can pick up dresses, gowns, pajamas, tops, bottoms, and other accessories at a fraction of the cost of purchasing new items.

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  • Baby gym-Baby gyms can be expensive to buy, but you can make your own for a fraction of the cost.

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  • Most people are happy to sell you their lightly-used children's clothing for a fraction of the price of new.

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  • Sometimes you can find used nursing bras for the fraction of the price of new ones.

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  • Still, with this in mind you can get the home of your dreams for a fraction of the cost that you would get through the traditional method of buying a home.

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  • Search the classified ads and moving sales for quality used patio sets for a fraction of the new cost.

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  • However, there are practice blades that you can purchase for a fraction of an actual broadhead price.

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  • At the Lenovo Outlet, you can get redistributed, refurbished, and scratched and dented models at a fraction of the retail cost.

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  • Set up alerts if you can for when the particular type of electronic or particular brand of item is listed or has a coupon available- you will get alerted and you can jump at the chance to buy the item you want for a fraction of the cost.

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  • This can be a great way to get an amazing deal since you are able to get an item direct from the manufacturer, with full manufacturers warranty, at a fraction of the cost.

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  • Securing a tax lien allows an investor to gain control over a real property with an investment that is a fraction of the market value of the property.

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  • It's a great way to get that luxury piece at a fraction of the cost.

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  • The hearing aids listed are just a sampling of various styles and brands, and just a fraction of what you'll find when you begin to shop.

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  • Instead of paying retail prices, you should consider visiting one to obtain a variety of the most fashionable products for a fraction of their normal cost.

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  • Dog Fence DIY is a website that will instruct you on how to build your own underground fence at a fraction of the cost of brand names like Invisible Fence.

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  • Many of these can be had for a fraction of the price of a new instrument.

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  • While commercially prepared raw pet food costs in excess of five dollars a pound, you can find inexpensive cuts of meat in your grocery store for a fraction of that cost.

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  • Homemade raw cat food costs just a fraction of what commercially prepared raw cat food does.

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  • The above offers are just a fraction of what may be available to you.

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  • With a cash back card, the company takes a fraction of that commission and gives it back to you.

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  • You can choose a new color or pattern, and it will look like you got a brand new couch for a fraction of the price!

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  • If you don't need your living room furniture right away, you may be able to score high quality furniture at a fraction of the price just by waiting and keeping your eyes open for liquidation sales.

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  • Visit Fine Wood Working for tips on ebonizing so that you can get the black dining room furniture you'd like, possibly even at a fraction of the cost.

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  • There are many reputable retailers that carry a full range of quality used furniture for your office, giving you a selection of high quality office furniture at a fraction of its original cost.

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  • Building materials that contain only a fraction of recycled materials may be trying to capitalize on the trend towards more sustainable design and offer very few concrete benefits.

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  • For furniture on a budget, don't forget to check retailers like Home Goods and Target, where you can often find French inspired pieces for a fraction of the cost.

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  • These ¼" sheets come in a wide variety of finishes at a fraction of the price of installing authentic beadboard.

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  • All were a fraction of the price at the design shops or even the "big-box" retailers.

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  • These stores are filled with furniture options that any top dollar retailer would be proud to put on their floor, but for a fraction of the price.

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  • If you're working with a limited budget, you can still achieve a customized look at a fraction of the cost.

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  • They protect furnishings from wear, tear and soiling, and can change the look and feel of a room for a fraction of the cost and effort of many other design methods.

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  • Best of all, these slipcovers are a small fraction of the price that you would pay for a new sofa!

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  • Acrylic and other synthetic fibers are often used as a way to offer a great looking rug for a fraction of the cost of a wool or silk rug.

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  • If you want to have a great look at a fraction of the cost, then a printed rug might be your best choice.

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  • Mark cosmetics are always in style, you'll find the latest seasonal colors found on the runway available to you as a Mark customer at a fraction of the cost without sacrificing quality.

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  • Sephora's Makeup Forever HD Microfinish in 5 Nip Slip - This highly blendable blush is a neutral pink that creates a soft, almost airbrushed look for a fraction of the price.

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  • Since you only pocket a fraction of the price paid by the client, selling your photos on microstock sites is not always very lucrative.

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  • If you're looking for a low fat stuffing recipe, this one is packed with delicious goodies while having only a fraction of the fat of regular stuffing.

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  • The beauty of digital scrapbooking is that you can create wonderful layouts online in a fraction of the time it takes to complete traditional scrapbook pages.

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  • By using a few simple creative techniques, you can make very memorable layouts for a fraction of what you'd spend on pre-made scrapbook embellishments.

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  • This method requires patience, but these retailers often sell items for just a fraction of their recommended price.

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  • It really is true that one man's trash is another man's treasure, and these treasures can cost a fraction of a new set of clothing.

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  • It's a great way to pick up the styles you love at a fraction of the price.

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  • There is a way, however, to get that designer look and feel for a fraction of the price; try a designer "inspired gown".

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  • You can also find a Kate Winslet red carpet design, in ice blue, for only a fraction of the cost at $225.00.

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  • Retailers are having huge sales that day and you could easily find prom dresses for a fraction of what you would pay during other times of the year.

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  • Outlet stores such as Beall's Outlet and Ross offer discounted formal wear for a fraction of what you would pay at the mall.

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  • Regular printed wedding invitations can be just as nice for a fraction of the price!

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  • Put on some festive music, purchase an assortment of snacks, and have your guests help you assemble your homemade wedding invitations in a fraction of the time it would take you to do it alone.

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  • With a little time and effort, couples can create spectacular invitations perfectly suited to their unique nuptials, and often at a fraction of the cost.

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  • What's more, depending on when you travel, Alaskan cruises often cost just a fraction of the price of traveling by land.

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  • You would benefit by getting a well socialized pet, and probably get it for a fraction of the price a puppy would cost.

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  • The Roadie can withstand up to 9,300 pounds in a crash, well beyond the strength of a human seat belt, and your dog weighs a fraction of the average human being.

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  • Remember, they are only a fraction of the entire population under production in your home.

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  • Learn how to install a Jacuzzi tub for a private getaway at the end of a long day -- at a fraction of the cost of a full sized hot tub.

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  • Adding solar deck lighting to your landscaping can make your home look as beautiful at night as in the daytime at a fraction of the cost.

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  • That's right, it looks like wood but is only a fraction of the cost.

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  • Clearance wood flooring is a great way to get quality wood flooring at a fraction of the cost of retail.

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  • They are inexpensive - Drop ceiling installation costs just a fraction of what a drywall ceiling costs.

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  • This in turn leads to a custom light placement and design at a fraction of the cost.

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  • On the other hand, installing storm windows costs far less, and installation takes just a fraction of the time.

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  • With a little time and effort, you can have a granite tile countertop that rivals the look of a slab for a fraction of the cost.

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  • Thermoplastic tiles come in the same decorative looks of ceramic, at a fraction of the cost.

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  • The sheets of tile are much larger, allowing you to install them in a fraction of the time that it would take for a comparable ceramic tile backsplash.

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  • If the motor is still good and you don't want to spring for a brand new fan, call the manufacturer and order replacement blades for a fraction of the price.

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  • The ring's setting is sterling silver, but it has a rhodium finish that gives the setting the appearance of white gold at a fraction of the cost.

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  • The wide availability of freshwater pearls has meant that pearl jewelry is much more accessible and beautiful items of jewelry are available for a fraction of the cost of expensive Akoya or Mikimoto pearls.

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  • A sterling silver bracelet can offer the same look as a 14KT white gold bracelet for a fraction of the cost.

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  • H&M - High-end designer looks at a fraction of the price, they also happen to have several items that can recreate a retro look in a flash.

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  • Men, there is no reason to pay full price for designer fashions when you can go shopping at guys fashion outlets and pay a fraction of the cost.

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  • No matter how you look at it, guys fashion outlets are a great way to have designer clothing at a fraction of the price.

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  • The Oakton brand men's shorts were as good as the similar-looking khaki shorts that were being sold at Banana Republic, but cost a fraction of that price.

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  • Today, more than ever, it is simpler to find well-priced men's clothing by reputable designers for a fraction of the retail price.

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  • Many times you can find gently worn items at a fraction of the original price.

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  • After that, it's possible for that same top to make its way to an outlet, at a fraction of its original price.

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  • This is just a fraction of the plus size fashions they offer.

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  • If you do your homework right, you can purchase some wonderful, high-quality clothing at a fraction of boutique or specialty shop prices.

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  • Smaller boutiques and specialty stores like bridal shops typically have off-season merchandise or customer returns that can be purchased for a fraction of the suggested retail.

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  • You may be able to find name brands at a fraction of the usual price.

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  • You will usually pay just a fraction of the retail cost of a pair of Maui Jims when you purchase replicas.

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  • The good news is that there are many inexpensive games that can be just as fun, but at a fraction of the price.

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  • That way you'll be able to get an excellent console for a fraction of its original price and can use that to experiment with a variety of games.

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  • Customers pay a fraction of the retail price to enjoy a game, while the creator gets profit from their labor.

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  • At that point, the memberships are sold for a small fraction of what the original purchaser paid.

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  • In many cases, the equipment might be either brand new or hardly used, and you can purchase it at a fraction of the cost you would pay at a retailer.

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  • However, a very small fraction have not.

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  • A very small fraction of hemoglobin spontaneously oxidizes per day, producing a protein of a slightly different structure called methemoglobin.

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