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decimal

In these cases the digit itself, or decimal multiples, seem to have been used.

2031198), the continual mention of large decimal numbers of shekels in the earlier books, and the certain fact of 100 shekels being = mina.

9770The first national coinage was begun in 1822, and the decimal system was adopted in 1863.

8052The first national coinage was begun in 1822, and the decimal system was adopted in 1863.

8052which stand as (1/6)th of the other decimal series based on the digit.

6357The great spread of the Phoenician weight on the Mediterranean, of the Persian in Asia Minor and of the Assyrian in Egypt are evident cases; and that the decimal weights of the laws of Manu (43) are decidedly not Assyrian or Persian, but on exactly the Phoenician standard, is a curious evidence of trade by water and not overland.

6258A decimal system of numeration was used, with numbers going up to io,000.

4440The power of io, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use.

4446The former translated the work into English; the latter was concerned with Napier in the change of the logarithms from those originally invented to decimal or common logarithms, and it is to him that the original calculation of the logarithmic tables now in use is mainly due.

4038And a strange division of the shekel in 10 (probably therefore connected with this decimal mina) is shown by a series of bronze weights (44) with four curved sides and marked with circles (British Museum, place unknown), which may be Romano-Gallic, averaging 125/10.

2627These examples show that Napier was in possession of all the conventions and attributes that enable the decimal point to complete so symmetrically our system of notation, viz.

2327These examples show that Napier was in possession of all the conventions and attributes that enable the decimal point to complete so symmetrically our system of notation, viz.

2327The explanation of this property of the base io is evident, for a change in the position of the decimal points amounts to multiplication or division by some power of 10, and this corresponds to the addition or subtraction of some integer in the case of the logarithm, the mantissa therefore remaining intact.

2223He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.

22254d.) is the standard coin, with a subsidiary decimal coinage.

2122To him are due the introduction of the decimal system of currency and the adoption of a system of protection to Canadian manufactures.

1919An account has now been given of Napier's invention and its publication, the transition to decimal logarithms, the calculation of the tables by Briggs, Vlacq and Gunter, as well as of the claims of Byrgius and the method of prosthaphaeresis.

1919He was one of the first members, and became president of the Bureau of Longitudes, took a prominent place at the Institute (founded in 1796), professed analysis at the Ecole Normale, and aided in the organization of the decimal system.

1819According to Krummel the following relations hold, good at 18° C. for the monochromatic light of the D line of the sodium spectrum in units of the fifth decimal place.

1724Seeing the good reasons for this digit having been exported to the West from Egypt--from the presence of the 18.23 cubit in Egypt, and from the 0.729 digit being the decimal base of the Greek long measures--it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot.

1620In tables of logarithms of numbers to base io the mantissa only is in general tabulated, as the characteristic of the logarithm of a number can always be written down at sight, the rule being that, if the number is greater than unity, the characteristic is less by unity than the number of digits in the integral portion of it, and that if the number is less than unity the characteristic is negative, and is greater by unity than the number of ciphers between the decimal point and the first significant figure.

16203 Besides his connexion with logarithms and improvements in the method of prosthaphaeresis, Byrgius has a share in the invention of decimal fractions.

1515The Greek system, however, adopted this foot as a basis for decimal multiplication, forming --

1519(arithmetic) elementary lessons on the notation of decimal fractions.

1519It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system.

1316Decimal fractions had been employed for the extraction of square roots.

1212Passing now to the invention of common or decimal logarithms, that is, to the transition from the logarithms originally invented by Napier to logarithms to the base io, the first allusion to a change of system occurs in the "Admonitio " on the last page of the Descriptio (1614), the concluding paragraph of which is " Verum si huius inventi usum eruditis gratum fore intellexero, dabo fortasse brevi (Deo aspirante) rationem ac methodum aut hunc canonem emendandi, aut emendatiorem de novo condendi, ut ita plurium Logistarum diligentia,limatior tandem et accuratior, quam unius opera fieri potuit, in lucem prodeat.

1217The accuracy of a meter is tested by drawing calibration curves showing the percentage departure from absolute accuracy in its reading for various decimal fractions of full load.

1116In 1782 he prepared an elaborate report on the coinage, suggesting the use of the decimal system and of the terms dollar and cent.

1011His table gives the logarithms of all numbers up to 2200, and of primes (and also of a great many composite numbers) from 2200 to 10,009, to 48 decimal places.

1016It originated in Babylonia as the foot of that system (24), in accordance with the sexary system applied to the early decimal division of the cubit.

914The Egyptians report the weight of a measure of various articles, amongst others water (6), but lay no special stress on it; and the fact that there is no measure of water equal to a direct decimal multiple of the weight-unit, except very high in the scale, does not seem as if the volume was directly based upon weight.

811The decimal point is, however, used systematically in the Constructio (1619), there being perhaps two hundred decimal points altogether in the book.

812Napier thus had complete command over decimal fractions and the use of the decimal point.

812The fact that when the base is io the mantissa of the logarithm is independent of the position of the decimal point in the number affords the chief reason for the choice of io as base.

812The coinage of Mexico, now concentrated at the mint in the capital (all others having been closed) is based (since November 28, 1867) on the decimal system - the peso being divided into 100 centavos - and consists of gold, silver, nickel and bronze coins, whose weight and fineness are determined by the monetary law of 1904.

814Troy weight was abolished, from the 1st of January 1879, by the Weights and Measures Act 1878, with the exception only of the Troy ounce, its decimal parts and multiples, legalized in 1853, 16 Vict.

79Since 1871 the decimal system of coinage, corresponding to that of the United States, has been the only one employed.

710Since 1871 the decimal system of coinage, corresponding to that of the United States, has been the only one employed.

710Briggs's Logarithmorum chilias prima, which contains the first published table of decimal or common logarithms, is only a small octavo tract of sixteen pages, and gives the logarithms of numbers from unity to 1000 to 14 places of decimals.

712These extracts contain all the original statements made by Napier, Robert Napier and Briggs which have reference to the origin of decimal logarithms. It will be seen that they are all in perfect agreement.

713These extracts contain all the original statements made by Napier, Robert Napier and Briggs which have reference to the origin of decimal logarithms. It will be seen that they are all in perfect agreement.

713The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.

717-- The ounce (480 gr.) and multiples and decimal parts of the ounce troy from 500 ounces to 0.001 oz.

610He again sat on the commission of 1799 for the construction of the metric system, and by his zealous advocacy of the decimal principle largely contributed to its adoption.

510When the base is to, the logarithms of all numbers in which the digits are the same, no matter where the decimal point may be, have the same mantissa; thus, for example, log 2.5613 =0-4084604, log 25.613 =1.4084604, log 2561300 = 6.4084604, &c.

48The Sum Will Be The Year Of The Christian Era, And The Day Of The Year Will Be Found By Multiplying The Decimal Figures By 365.

48Decimal or Briggian Antilogarithms. - In the ordinary tables of logarithms the natural numbers are all integers, while the logarithms tabulated are incommensurable.

37This is also evidently the Olympic cubit; and, in pursuance of the decimal multiple of the digit found in Egypt and Persia, the cubit of 25 digits was (1/4)th of the orguia of 100 digits, the series being --

38This is also evidently the Olympic cubit; and, in pursuance of the decimal multiple of the digit found in Egypt and Persia, the cubit of 25 digits was (1/4)th of the orguia of 100 digits, the series being --

38r= io, we get the ordinary expression of P/Q as an integer and a decimal; but, if P/Q were equal to 1/3, we could not express it as a decimal with a finite number of figures.

39Briggs appreciated clearly the advantages of a centesimal division of the quadrant, and by dividing the degree into hundredth parts instead of into minutes, made a step towards a reformation in this respect, and but for the appearance of Vlacq's work the decimal division of the degree might have become recognized.

39r= io, we get the ordinary expression of P/Q as an integer and a decimal; but, if P/Q were equal to 1/3, we could not express it as a decimal with a finite number of figures.

39It was a long time before decimal arithmetic came into general use, and all through the 17th century exponential marks were in common use.

310The banking system of the country was put on a sound footing by a series of acts culminating in 1871, and in the same year a uniform system of decimal currency was established for the whole Dominion.

28There seems but little doubt that Napier was the first to make use of a decimal separator, and it is curious that the separator which he used, the point, should be that which has been ultimately adopted, and after a long period of partial disuse.

29The voters were to choose one-tenth of their number (notabilities of the commune); one-tenth of these would form the notabilities of the department; while by a similar decimal sifting, the notabilities of the nation were selected.

29There seems but little doubt that Napier was the first to make use of a decimal separator, and it is curious that the separator which he used, the point, should be that which has been ultimately adopted, and after a long period of partial disuse.

29The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619).

00The system is decimal; thus 100 pfcnnige = I mark, 1000 pfennige = the gold krone (or crown), and Id.

00Mat hematics.T he Egyptian notation for whole numbers was decimal, each power of 10 up to 100,000 being represented by a different figure, on much the same principle as the Roman numerals.

00either a decimal or a doubling system or a combination of the two.

00In the succeeding session his service was marked by a report, from which resulted the present monetary system of the United States (the fundamental idea of its decimal basis being due, however, to Gouverneur Morris); and by the honour of reporting the first definitely formulated plan for the government of the western territories,' that embodied in the ordinance of 1784.

00focal length a discrepancy of I unit in the 3rd decimal place in the above proportional figures would cause a linear error in the focus for that colour of only about .025 in., so that the largest deviation implied by the tables would be a focus for the extreme violet H ray about 037 longer than the normal.

00Decimal coinage >>

00of which the successive convergents are 3 22 333 355 103993 &c., I' 7' 106' 113' 33102' the fourth of which is accurate to the sixth decimal place, since the error lies between I /g4g5 or.

00The French decimal system is in use for weights and measures, together with Turkish standards.

00When we turn to the social divisions we find in Domesday and other documents classes of society in these districts bearing purely Norse names, dreng, karl, karlman, bonde, thrall, lysing, hold; in the system of taxation we have an assessment by carucates and not by hides and virgates, and the duodecimal rather than the decimal system of reckoning.

00Division by Decimal 6.9 79.

00On the continent of Europe the figures are taken in sets of three, but are merely spaced, the comma being used at the end of a number to denote the commencement of a decimal.

00Decimal Notation of Percentage.

00Decimal Fractions.

00A 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.

00A 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.

00Hence the successive figures after the decimal point have the same relation to each other and to the figures before the point as if the point did not exist.

00Fractions other than decimal fractions are usually called vulgar fractions.

00Decimal Numbers.

00A number made up in this way may be called a decimal number, or, more briefly, a decimal.

00if one has more figures after the decimal point than the other, we must add sufficient o's to the latter to make the numbers of figures equal.

00To divide one decimal by another, we must reduce them to the same denomination, as explained in § 76, and then omit the decimal points.

00Under one system, for instance, the continued sum 5 + X 5 + 8 X 7 X 5 would be denoted 7 by 8 I 5; this is somewhat similar in principle to a decimal notation, but with digits taken in the reverse order.

00Even where the decimal notation would seem to arise naturally, as in the case of approximate extraction of a square root, the portion which might have been expressed as a decimal was converted into sexagesimal fractions.

001585 that a decimal notation was published by Simon Stevinus of Bruges.

00The present decimal notation, which is a development of that of Stevinus, was first used in 1617 by H.

00The numbers (integral or decimal) by which we represent the results of arithmetical operations are often only approximately correct.

00If the number of decimal places to which a result is to be accurate is determined beforehand, it is usually not necessary in the actual working to go to more than two or three places beyond this.

002, as base, and take as indices the successive decimal numbers to any particular number of places of decimals, we get a series of antilogarithms of the indices to this base.

00The series is formed by successive multiplication, and any antilogarithm to a larger number of decimal places is formed from it in the same way by multiplication.

00it means a shifting of the decimal point.

00fractional or decimal) numbers not shown in the table.

00For 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.

00A sum of money cannot be expressed exactly as a decimal of LI unless it is a multiple of 4d.

00Division 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.

00A better method is to ignore the positions of the decimal points, and multiply the numbers as if they were decimals between I and i o.

00Thus, 0859 to multiply 2 7.343 by 3.14159 2 7 to one decimal place, we require 2+ I+ I =4 figures in the product.

00The result is 085.9 = 8 5.9, the position of the decimal point being determined by counting the figures before the decimal points in the original numbers.

00A decimal is of course a series of this kind, e.g.

003.1416 is a little less than 3 + 7 - s o Recurring Decimals are a particular kind of series, which arise from the expression of a fraction as a decimal.

00If 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.

00The system is decimal throughout.

00In these carefully written papers he treats a great variety of topics relating to astronomy, chronology, decimal coinage, life assurance, bibliography and the history of science.

00Considerable labour was spent by De Morgan upon the subject of decimal coinage.

00His evidence on this subject was sought by the Royal Commission, and, besides constantly supporting the Decimal Association in periodical publications, he published several separate pamphlets on the subject.

00Its usefulness arises from its decimal or centesimal division, and the fact that to square chains make an acre.

00It was also proposed to divide the day on the decimal system, but this arrangement was found to be highly inconvenient and it was never put into practice.

00A Decimal Association was formed in 1854, but did not make very much headway.

00See also Decimal Coinage and Weights And Measures.

00£150,000 989,000 291,000 367,000.13,516,000 192,000.2,300,000 3,767,000 In 1875 Servia adopted the decimal system for money, weights and measures, which came into actual use in 1883.

00Currencv, Weidhts and Measures.The metric system of weights and measures was officially adopted in Spain in 1859 and the decimal monetary system in 1871.

00Before the introduction of the decimal monetary system the peseta was the fifth part of a peso dare, which was equal to 20 re i/es de velion, or rather more than a 5-franc piece.

00Most of Quinn's numbers carried out four decimal points, such as "44.9064" but others extended as high as six places.

00At the nike and sources and the reports Bennett next decimal place.

00Scotch salmon at Billingsgate was then fetching 2s 6d [15p in decimal coinage] a pound wholesale.

00Enter the origin and length as long integer constants in either decimal, octal, or hexadecimal (standard C syntax ).

00During the 1960s the Irish government decided to adopt a decimal currency like many of its European neighbors.

00Query: Does anyone know how to do the recurring decimal in Word, where you put the dot over the number?

00You can do this using either decimal or hex numbers.

00decimal coded, in units of bps, e.g. 2400 specifies the lowest rate to be 2400.

00A PL /SQL function to convert decimal to hex is described in a separate note.

00The PRM says " Use of this expanded format allows conversion from extended precision to packed decimal and back again without loss of accuracy.

00An exact decimal is a decimal number that does not go on forever.

00decimal digits of Pi correct to 210 places.

00decimalFormat does not decide whether to return a Double or a Long based on the presence of a decimal separator in the source string.

00decimal notation numbers are:- 10 0 10.

00decimal fractions.

00decimal integer in the range from 1 to 255.

00decimal coinage, Arnold Machin was commissioned to prepare a new coin portrait of the Queen.

00Hindu counting system was purely decimal and distinct symbols for the numbers 1 - 9 existed already.

00Decimal notation decimal notation Decimal numbers consist of one or more of the following:- An optional integer part to the left of any decimal point.

00MM is the month of the year, expressed with two decimal digits.

00Large results - where the number of digits to the left of the decimal point exceeds the current setting of numeric digits.

00Day of the week is represented by one decimal digit.

00ecliptic longitude of the object in decimal degrees.

00The only decimal separator known to javascript (new releases possibly excepted) is the decimal point, " .

00Decimal Arithmetic Most computers today support binary floating-point in hardware.

00In the example you quote £ 10.31 the " .31 " is a decimal fraction of a pound, not of the pence.

00galactic latitude of the object in decimal degrees.

00It is not, generally, possible to use hexadecimal or decimal constants in this fashion.

00They take numbers as decimal unless starting with 0x (or 0X ), meaning hexadecimal; a leading zero does not mean octal.

00Note the way that decimal and octal integers are read in by grammar rules.

00The skip argument is normally interpreted as a posi- tive decimal integer.

00The Astronomical Almanac reports the galactic latitude of the object in decimal degrees.

00latitude of the object in decimal degrees.

00numeric literals containing a decimal point or an exponent sign yield floating point numbers.

00The Astronomical Almanac reports the galactic longitude of the object in decimal degrees.

00The Astronomical Almanac reports the ecliptic longitude of the object in decimal degrees.

00longitude in decimal degrees to decimal hours divide by 15.

00longitude of the object in decimal degrees.

00We shall use decimal notation for units in this module.

00IP addresses are normally written in a format known as " dotted decimal notation " .

00A number expressed in exponential notation consists of the following:- A decimal number.

00numeric literals containing a decimal point or an exponent sign yield floating point numbers.

00obverse changed in line with the remainder of the decimal coinage.

00The conversion types are: Conversion Meaning Notes d Signed integer decimal. i Signed integer decimal. o Unsigned octal.

00All numbers can be expressed in 6 formats: decimal, octal, hexadecimal, binary, with fixed point, or scientific.

00I can calculate pi in my head to over six hundred decimal places.

00An object of diameter 1 meter would only improve the error to give pi to about 1 more decimal place.

00precessed epoch in decimal years.

00recurring decimal in Word, where you put the dot over the number?

00LC _ NUMERIC specifies the decimal and thou- sands delimiters.

00decimalFormat does not decide whether to return a Double or a Long based on the presence of a decimal separator in the source string.

00continuous variates could take any value in an interval, tho measurement accuracy limits the number of decimal places recorded.

00This is silly, as you might well want to give the decimal value for a low-end wingding or other symbol.

00The logarithms introduced by Napier in the Descriptio are not the same as those now in common use, nor even the same as those now called Napierian or hyperbolic logarithms. The change from the original logarithms to common or decimal logarithms was made by both Napier and Briggs, and the first tables of decimal logarithms were calculated by Briggs, who published a small table, extending to 1000, in 1617, and a large work, Arithmetica Logarithmica, 1 containing logarithms of numbers to 30,000 and from 90,000 to Ioo,000, in 1624.

00To Napier seems to be due the first use of the decimal point in arithmetic. Decimal fractions were first introduced by Stevinus in his tract La Disme, published in 1585, but he used cumbrous exponents (numbers enclosed in circles) to distinguish the different denominations, primes, seconds, thirds, &c. Thus, for example, he would have written 123.456 as 123@4050603.

00This single instance of the use of the decimal point in the midst of an arithmetical process, if it stood alone, would not suffice to establish a claim for its introduction, as the real introducer of the decimal point is the person who first saw that a point or line as separator was all that was required to distinguish between the integers and fractions, and used it as a permanent notation and not merely in the course of performing an arithmetical operation.

00The decimal point is, however, used systematically in the Constructio (1619), there being perhaps two hundred decimal points altogether in the book.

00(1) he saw that a point or separatrix was quite enough to separate integers from decimals, and that no signs to indicate primes, seconds, &c., were required; (2) he used ciphers after the decimal point and preceding the first significant figure; and (3) he had no objection to a decimal standing by itself without any integer.

00Napier thus had complete command over decimal fractions and the use of the decimal point.

00It was a long time before decimal arithmetic came into general use, and all through the 17th century exponential marks were in common use.

00In 1838, and again in 1843, he was one of the commissioners for standards of weights and measures; and he also furnished valuable information to the commissioners on decimal coinage.

00A decimal system of numeration was used, with numbers going up to io,000.

00The voters were to choose one-tenth of their number (notabilities of the commune); one-tenth of these would form the notabilities of the department; while by a similar decimal sifting, the notabilities of the nation were selected.

00He again sat on the commission of 1799 for the construction of the metric system, and by his zealous advocacy of the decimal principle largely contributed to its adoption.

00He was one of the first members, and became president of the Bureau of Longitudes, took a prominent place at the Institute (founded in 1796), professed analysis at the Ecole Normale, and aided in the organization of the decimal system.

00to 175Ã‚° F., corresponding to decimal parts of an inch of mercury of the vacuum gauge.

00In the Swedish House of Nobles his contributions to political discussion had great influence, and he dealt with such subjects as the currency, the decimal system, the balance of trade and the liquor laws (where he was the pioneer of the Gothenburg system) with marked ability.

00To him are due the introduction of the decimal system of currency and the adoption of a system of protection to Canadian manufactures.

00According to Krummel the following relations hold, good at 18Ã‚° C. for the monochromatic light of the D line of the sodium spectrum in units of the fifth decimal place.

004d.) is the standard coin, with a subsidiary decimal coinage.

00In 1782 he prepared an elaborate report on the coinage, suggesting the use of the decimal system and of the terms dollar and cent.

00The accuracy of a meter is tested by drawing calibration curves showing the percentage departure from absolute accuracy in its reading for various decimal fractions of full load.

00During the Revolution, he was one of the three members of the council established to introduce the decimal system, and he was also a member of the commission appointed to determine the length of the metre, for which purpose the calculations, &c., connected with the arc of the meridian from Barcelona to Dunkirk were revised.

00Troy weight was abolished, from the 1st of January 1879, by the Weights and Measures Act 1878, with the exception only of the Troy ounce, its decimal parts and multiples, legalized in 1853, 16 Vict.

00The great spread of the Phoenician weight on the Mediterranean, of the Persian in Asia Minor and of the Assyrian in Egypt are evident cases; and that the decimal weights of the laws of Manu (43) are decidedly not Assyrian or Persian, but on exactly the Phoenician standard, is a curious evidence of trade by water and not overland.

00The Egyptians report the weight of a measure of various articles, amongst others water (6), but lay no special stress on it; and the fact that there is no measure of water equal to a direct decimal multiple of the weight-unit, except very high in the scale, does not seem as if the volume was directly based upon weight.

00It originated in Babylonia as the foot of that system (24), in accordance with the sexary system applied to the early decimal division of the cubit.

00In these cases the digit itself, or decimal multiples, seem to have been used.

00The Greek system, however, adopted this foot as a basis for decimal multiplication, forming --

00which stand as (1/6)th of the other decimal series based on the digit.

00Seeing the good reasons for this digit having been exported to the West from Egypt--from the presence of the 18.23 cubit in Egypt, and from the 0.729 digit being the decimal base of the Greek long measures--it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot.

00It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system.

008), the continual mention of large decimal numbers of shekels in the earlier books, and the certain fact of 100 shekels being = mina.

00And a strange division of the shekel in 10 (probably therefore connected with this decimal mina) is shown by a series of bronze weights (44) with four curved sides and marked with circles (British Museum, place unknown), which may be Romano-Gallic, averaging 125/10.

00-- 100 feet, 66 feet or a chain of 100 links, rod, pole, or perch, measures from 10 feet to 1 foot; 18 inches; yard of 36 inches, 1/2, 1/4, 18, 1/16 yard, nail, inch, and duodecimal, decimal, and binary parts of an inch.

00-- The ounce (480 gr.) and multiples and decimal parts of the ounce troy from 500 ounces to 0.001 oz.

00(arithmetic) elementary lessons on the notation of decimal fractions.

00When the base is to, the logarithms of all numbers in which the digits are the same, no matter where the decimal point may be, have the same mantissa; thus, for example, log 2.5613 =0-4084604, log 25.613 =1.4084604, log 2561300 = 6.4084604, &c.

00The fact that when the base is io the mantissa of the logarithm is independent of the position of the decimal point in the number affords the chief reason for the choice of io as base.

00The explanation of this property of the base io is evident, for a change in the position of the decimal points amounts to multiplication or division by some power of 10, and this corresponds to the addition or subtraction of some integer in the case of the logarithm, the mantissa therefore remaining intact.

00In tables of logarithms of numbers to base io the mantissa only is in general tabulated, as the characteristic of the logarithm of a number can always be written down at sight, the rule being that, if the number is greater than unity, the characteristic is less by unity than the number of digits in the integral portion of it, and that if the number is less than unity the characteristic is negative, and is greater by unity than the number of ciphers between the decimal point and the first significant figure.

00The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.

00The former translated the work into English; the latter was concerned with Napier in the change of the logarithms from those originally invented to decimal or common logarithms, and it is to him that the original calculation of the logarithmic tables now in use is mainly due.

00Briggs's Logarithmorum chilias prima, which contains the first published table of decimal or common logarithms, is only a small octavo tract of sixteen pages, and gives the logarithms of numbers from unity to 1000 to 14 places of decimals.

00Briggs appreciated clearly the advantages of a centesimal division of the quadrant, and by dividing the degree into hundredth parts instead of into minutes, made a step towards a reformation in this respect, and but for the appearance of Vlacq's work the decimal division of the degree might have become recognized.

00Passing now to the invention of common or decimal logarithms, that is, to the transition from the logarithms originally invented by Napier to logarithms to the base io, the first allusion to a change of system occurs in the "Admonitio " on the last page of the Descriptio (1614), the concluding paragraph of which is " Verum si huius inventi usum eruditis gratum fore intellexero, dabo fortasse brevi (Deo aspirante) rationem ac methodum aut hunc canonem emendandi, aut emendatiorem de novo condendi, ut ita plurium Logistarum diligentia,limatior tandem et accuratior, quam unius opera fieri potuit, in lucem prodeat.

00The power of io, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use.

00An account has now been given of Napier's invention and its publication, the transition to decimal logarithms, the calculation of the tables by Briggs, Vlacq and Gunter, as well as of the claims of Byrgius and the method of prosthaphaeresis.

003 Besides his connexion with logarithms and improvements in the method of prosthaphaeresis, Byrgius has a share in the invention of decimal fractions.

00Decimal or Briggian Antilogarithms. - In the ordinary tables of logarithms the natural numbers are all integers, while the logarithms tabulated are incommensurable.

00His table gives the logarithms of all numbers up to 2200, and of primes (and also of a great many composite numbers) from 2200 to 10,009, to 48 decimal places.

00The coinage of Mexico, now concentrated at the mint in the capital (all others having been closed) is based (since November 28, 1867) on the decimal system - the peso being divided into 100 centavos - and consists of gold, silver, nickel and bronze coins, whose weight and fineness are determined by the monetary law of 1904.

00He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.

00The banking system of the country was put on a sound footing by a series of acts culminating in 1871, and in the same year a uniform system of decimal currency was established for the whole Dominion.

00The Sum Will Be The Year Of The Christian Era, And The Day Of The Year Will Be Found By Multiplying The Decimal Figures By 365.

00Decimal fractions had been employed for the extraction of square roots.

00some five centuries before his time, but nobody before Stevinus established their daily use; and so well aware was he of the importance of his innovation that he declared the universal introduction of decimal coinage, measures and weights to be only a question of time.

00The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619).

00The rent charge is apportioned on all the lands liable in the parish, and such apportionment may be altered or a new one made: and the value of the rent charge is fixed at the value (at the time of confirmation of the apportionment) of the number of imperial bushels and decimal parts of bushels of wheat, barley and oats as the same would have purchased at the prices so ascertained by the advertisement (of prices of corn) to be published immediately after the passing of the act 6 & 7 Will.

00The system is decimal; thus 100 pfcnnige = I mark, 1000 pfennige = the gold krone (or crown), and Id.

00Mat hematics.T he Egyptian notation for whole numbers was decimal, each power of 10 up to 100,000 being represented by a different figure, on much the same principle as the Roman numerals.

00either a decimal or a doubling system or a combination of the two.

00In the succeeding session his service was marked by a report, from which resulted the present monetary system of the United States (the fundamental idea of its decimal basis being due, however, to Gouverneur Morris); and by the honour of reporting the first definitely formulated plan for the government of the western territories,' that embodied in the ordinance of 1784.

00focal length a discrepancy of I unit in the 3rd decimal place in the above proportional figures would cause a linear error in the focus for that colour of only about .025 in., so that the largest deviation implied by the tables would be a focus for the extreme violet H ray about 037 longer than the normal.

00Decimal coinage >>

00of which the successive convergents are 3 22 333 355 103993 &c., I' 7' 106' 113' 33102' the fourth of which is accurate to the sixth decimal place, since the error lies between I /g4g5 or.

00The French decimal system is in use for weights and measures, together with Turkish standards.

00When we turn to the social divisions we find in Domesday and other documents classes of society in these districts bearing purely Norse names, dreng, karl, karlman, bonde, thrall, lysing, hold; in the system of taxation we have an assessment by carucates and not by hides and virgates, and the duodecimal rather than the decimal system of reckoning.

00Division by Decimal 6.9 79.

00On the continent of Europe the figures are taken in sets of three, but are merely spaced, the comma being used at the end of a number to denote the commencement of a decimal.

00Decimal Notation of Percentage.

00Decimal Fractions.

00A 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.

00A 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.

00Hence the successive figures after the decimal point have the same relation to each other and to the figures before the point as if the point did not exist.

00Fractions other than decimal fractions are usually called vulgar fractions.

00Decimal Numbers.

00A number made up in this way may be called a decimal number, or, more briefly, a decimal.

00if one has more figures after the decimal point than the other, we must add sufficient o's to the latter to make the numbers of figures equal.

00To divide one decimal by another, we must reduce them to the same denomination, as explained in § 76, and then omit the decimal points.

00Under one system, for instance, the continued sum 5 + X 5 + 8 X 7 X 5 would be denoted 7 by 8 I 5; this is somewhat similar in principle to a decimal notation, but with digits taken in the reverse order.

00Even where the decimal notation would seem to arise naturally, as in the case of approximate extraction of a square root, the portion which might have been expressed as a decimal was converted into sexagesimal fractions.

001585 that a decimal notation was published by Simon Stevinus of Bruges.

00The present decimal notation, which is a development of that of Stevinus, was first used in 1617 by H.

00The numbers (integral or decimal) by which we represent the results of arithmetical operations are often only approximately correct.

00If the number of decimal places to which a result is to be accurate is determined beforehand, it is usually not necessary in the actual working to go to more than two or three places beyond this.

002, as base, and take as indices the successive decimal numbers to any particular number of places of decimals, we get a series of antilogarithms of the indices to this base.

00The series is formed by successive multiplication, and any antilogarithm to a larger number of decimal places is formed from it in the same way by multiplication.

00it means a shifting of the decimal point.

00fractional or decimal) numbers not shown in the table.

00For 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.

00A sum of money cannot be expressed exactly as a decimal of LI unless it is a multiple of 4d.

00Division 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.

00A better method is to ignore the positions of the decimal points, and multiply the numbers as if they were decimals between I and i o.

00Thus, 0859 to multiply 2 7.343 by 3.14159 2 7 to one decimal place, we require 2+ I+ I =4 figures in the product.

00The result is 085.9 = 8 5.9, the position of the decimal point being determined by counting the figures before the decimal points in the original numbers.

00A decimal is of course a series of this kind, e.g.

003.1416 is a little less than 3 + 7 - s o Recurring Decimals are a particular kind of series, which arise from the expression of a fraction as a decimal.

00If 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.

00The system is decimal throughout.

00In these carefully written papers he treats a great variety of topics relating to astronomy, chronology, decimal coinage, life assurance, bibliography and the history of science.

00Considerable labour was spent by De Morgan upon the subject of decimal coinage.

00His evidence on this subject was sought by the Royal Commission, and, besides constantly supporting the Decimal Association in periodical publications, he published several separate pamphlets on the subject.

00Its usefulness arises from its decimal or centesimal division, and the fact that to square chains make an acre.

00It was also proposed to divide the day on the decimal system, but this arrangement was found to be highly inconvenient and it was never put into practice.

00A Decimal Association was formed in 1854, but did not make very much headway.

00See also Decimal Coinage and Weights And Measures.

00£150,000 989,000 291,000 367,000.13,516,000 192,000.2,300,000 3,767,000 In 1875 Servia adopted the decimal system for money, weights and measures, which came into actual use in 1883.

00Currencv, Weidhts and Measures.The metric system of weights and measures was officially adopted in Spain in 1859 and the decimal monetary system in 1871.

00Before the introduction of the decimal monetary system the peseta was the fifth part of a peso dare, which was equal to 20 re i/es de velion, or rather more than a 5-franc piece.

00LC _ NUMERIC specifies the decimal and thou- sands delimiters.

00Continuous variates could take any value in an interval, tho measurement accuracy limits the number of decimal places recorded.

00This is silly, as you might well want to give the decimal value for a low-end WingDing or other symbol.

00The nonfiction section of the library is ordered by the Dewey Decimal System.

00Finally, just decimal numbers would be used.

00Because one carat solitaire diamonds are far more rare than smaller sizes - particularly if they do not have flaws or inclusions - there is a hefty price jump once that decimal point is crossed.

00For grading purposes and diamond certification, gems are measured to three decimal places, though that measurement may then be rounded to two decimal places for convenience.

00When entering a fraction of an amount use a decimal not a fraction.

00The answer for graphics designers came in the form of hexadecimal notation - which starts with the digits 0-9 just like decimal number systems, but instead of going on to "10" it instead goes into the letters A-F.

00So to write the decimal number "10" in hexadecimal notation, it would be "A".

00Keep in mind that middle number is not 64 (in decimal format) - it is actually 100, when translated into decimal form.

00If they'd stuck with the decimal system, that would have severely limited the number of shades of color available.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.