PRACTICAL ARITHMETIC is the art of numbering, or of performing calculations by numbers.. ΝΟΤΑΤΙΟ Ν. N number, either by words, or characters. TOTATION is the expreffing of any propofed All numbers are expreffible by these ten characters or figures, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, or cypher: and the usual method of notation by figures is fo contrived, that any character is increased in its value in a tenfold proportion for every place it is removed to the left among the other figures with which it is connected; fo in thefe figures 333, the first 3 (reckoning from the right to the left) is 3 ones, but the fecond is 3 tens, and the third is 3 hundreds; alfo in these 2759, the 9 represents 9 ones, but the 5 reprefents 5 tens, the 7 is 7 hundreds, and the 2 is 2 thousand. And though the cypher fignify nought of itself, yet when put on the right of any of the other figures, it increaseth their value in the fame tenfold proportion above defcribed; thus, though 2 standing alone, or in the firft place, reprefent only 2 ones, yet when a cypher is wrote on the right of it, thus 20, it represents 2 tens or twenty; and if another cypher be affixed, thus 200, it will reprefent 2 hundreds. For the more eafy reading of large numbers, when they are expreffed by figures, they are divided, from the right hand towards the left, into periods and half-periods, each half-period confifting of three figures; the common name of the first period being units or ones; of the fecond, millions; of the third, billions; of the fourth, trillions, B. &e. &c. Alfo the first half of any period is fo many ones of ́it, but the latter half is fo many thousands of it. The following example exhibits a fummary of this whole doctrine. Quintillions Quadrillions Trillions Billions Millions Units th. un. th. un. th. un. 473,829. 759,761. 235,871. Note, The first nine characters are called digits, and fometimes fignificant figures, to diftingu fh them from the cypher, which of itself is infignificant. Alfo, a number expreffing a quantity of one name or denomination, is called a fimple number, as 20 pounds, or 17 gallons, or 5 days; and that reprefenting a quantity of feveral names, is called a compound number, as 13 pounds 5 Shillings and 6 pence, or 17 gallons and two pints, or 3 hours and 50 minutes. th. un. th. un. C. x . c. x. u. 296;473. 913,651. 437,2 56. 1. Having any number propofed in words, to express the Jame in figures. RULE. Write down cyphers to fo many periods and places as are named in the given number; then beginning at the left, obferve at each place what fignificant figure is named, and, taking away the cypher, write the fignificant figure in its place. EXAMPLES. 1. Exprefs in figures, Four thousand, one hundred, and feventy-three. 2. Write down in figures, Twenty-three millions, two hundred and fix thousand, nine hundred and thirty. 3. Write in figures, Four thousand and twenty-five millions, one hundred and three thoufand, and fix. 4. Exprefs in figures, Two hundred feventeen thousand and fifty millions,eight thoufand,feven hundred,andfixteen. 5. Write down in figures, Seventy thousand billions, one hundred three thoufand and fifty millions, three thoufand and eight. 6. Exprefs in figures, Eight hundred trillions, one hundred feventy-five thousand feven hundred and fortycight billions, three hundred thousand millions, five thoufand, and feventy. II. Having any number expressed in figures, to read the fame, or exprefs it in words. RULE. RULE. Divide the figures in the given number, as in the general example, into periods and half-periods, by any convenient marks; then, beginning at the left, the figures are thus read; viz. the firft figure of each half-period is named by itself with the word hundreds, but the other two are named together; and at the end of the first half of each period, the word thoufands is named, but at the end of the other half, the common name of the whole period, except it be the units period, whofe name is not expressed EXAMPLES. 1. Let it be required to exprefs in words, 17359- 4. Exprefs in words, 102003000400. 5. Write in worls, 2073000091630702. . 6. Write down in words, 503002786940003. A SYNOPSIS of the ROMAN NOTATION. } I 2 3= 4: II As often as any character is repeated, so many times its value is repeated. IIII or IV A lefs character before a greater diminishes its value. 5=V 6 VI 500 A lefs character after a greater increases its value. Dor I: for every affixed, this becomes 10 times fo many. 1000 V or CI: for every C &, put one at each end, 5000 6000-VI 1000 fold. 10000 or CCIɔɔ B 2 50000 |