# Decimal Sentence Examples

In these cases the digit itself, or

**decimal**multiples, seem to have been used.The first national coinage was begun in 1822, and the

**decimal**system was adopted in 1863.Day of the week is represented by one

**decimal**digit.The only

**decimal**separator known to javascript (new releases possibly excepted) is the**decimal**point, " .Large results - where the number of digits to the left of the

**decimal**point exceeds the current setting of numeric digits.AdvertisementIn the example you quote £ 10.31 the " .31 " is a

**decimal**fraction of a pound, not of the pence.I can calculate pi in my head to over six hundred

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

**decimal**place.This is silly, as you might well want to give the

**decimal**value for a low-end wingding or other symbol.The 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.AdvertisementTo 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.This 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.In 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.In 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.During 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.AdvertisementA

**decimal**system of numeration was used, with numbers going up to io,000.In 1782 he prepared an elaborate report on the coinage, suggesting the use of the

**decimal**system and of the terms dollar and cent.Troy 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.Seeing 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.It is remarkable how near this early

**decimal**system of Germany and Britain is the double of the modern**decimal**metric system.AdvertisementThe 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.Since 1871 the

**decimal**system of coinage, corresponding to that of the United States, has been the only one employed.**Decimal**fractions had been employed for the extraction of square roots.The 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).The system is

**decimal**; thus 100 pfcnnige = I mark, 1000 pfennige = the gold krone (or crown), and Id.AdvertisementMat 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.In 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.The French

**decimal**system is in use for weights and measures, together with Turkish standards.When 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.On 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**.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.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.Hence 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.Fractions other than

**decimal**fractions are usually called vulgar fractions.A number made up in this way may be called a

**decimal**number, or, more briefly, a**decimal**.To divide one

**decimal**by another, we must reduce them to the same denomination, as explained in § 76, and then omit the**decimal**points.Under 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.Even 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.The numbers (integral or

**decimal**) by which we represent the results of arithmetical operations are often only approximately correct.If 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.The 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.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.A sum of money cannot be expressed exactly as a

**decimal**of LI unless it is a multiple of 4d.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.A 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.Thus, 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.The 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.A

**decimal**is of course a series of this kind, e.g.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.The system is

**decimal**throughout.In 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.Considerable labour was spent by De Morgan upon the subject of

**decimal**coinage.His 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.Its usefulness arises from its

**decimal**or centesimal division, and the fact that to square chains make an acre.It 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.A

**Decimal**Association was formed in 1854, but did not make very much headway.Currencv, Weidhts and Measures.The metric system of weights and measures was officially adopted in Spain in 1859 and the

**decimal**monetary system in 1871.Before 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.Most of Quinn's numbers carried out four

**decimal**points, such as "44.9064" but others extended as high as six places.Scotch salmon at Billingsgate was then fetching 2s 6d [15p in

**decimal**coinage] a pound wholesale.During the 1960s the Irish government decided to adopt a

**decimal**currency like many of its European neighbors.You can do this using either

**decimal**or hex numbers.A PL /SQL function to convert

**decimal**to hex is described in a separate note.The PRM says " Use of this expanded format allows conversion from extended precision to packed

**decimal**and back again without loss of accuracy.An exact

**decimal**is a**decimal**number that does not go on forever.Hindu counting system was purely

**decimal**and distinct symbols for the numbers 1 - 9 existed already.It is not, generally, possible to use hexadecimal or

**decimal**constants in this fashion.They take numbers as

**decimal**unless starting with 0x (or 0X ), meaning hexadecimal; a leading zero does not mean octal.Note the way that

**decimal**and octal integers are read in by grammar rules.The skip argument is normally interpreted as a posi- tive

**decimal**integer.The Astronomical Almanac reports the galactic latitude of the object in

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

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

**decimal**degrees.We shall use

**decimal**notation for units in this module.Because 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.The 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.Continuous variates could take any value in an interval, tho measurement accuracy limits the number of

**decimal**places recorded.This is silly, as you might well want to give the

**decimal**value for a low-end WingDing or other symbol.The nonfiction section of the library is ordered by the Dewey

**Decimal**System.Finally, just

**decimal**numbers would be used.For 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.When entering a fraction of an amount use a

**decimal**not a fraction.So to write the

**decimal**number "10" in hexadecimal notation, it would be "A".If they'd stuck with the

**decimal**system, that would have severely limited the number of shades of color available.The

**decimal**point is, however, used systematically in the Constructio (1619), there being perhaps two hundred**decimal**points altogether in the book.Napier thus had complete command over

**decimal**fractions and the use of the**decimal**point.He 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.The 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.The Greek system, however, adopted this foot as a basis for

**decimal**multiplication, forming --And 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.When 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.The 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.The 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.The 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.**Decimal**or Briggian Antilogarithms. - In the ordinary tables of logarithms the natural numbers are all integers, while the logarithms tabulated are incommensurable.He 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.The 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.Keep in mind that middle number is not 64 (in

**decimal**format) - it is actually 100, when translated into**decimal**form.He 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.To him are due the introduction of the

**decimal**system of currency and the adoption of a system of protection to Canadian manufactures.This 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 --Briggs'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.There 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.The 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.The 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.The 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.It 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.The 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.It was a long time before

**decimal**arithmetic came into general use, and all through the 17th century exponential marks were in common use.Briggs 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.These 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.An 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.His 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.The 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.In 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.Passing 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.These 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.The 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.