gar fraction it is written down as it comes from divifion; thus, if 37 was to be divided by 5, the quotient wou'd be more than 7, and lefs than 8; that is, it would be 7 3, or 7 times and 2 parts of 5: Here, the uppermost number of the fraction is call'd the Numerator, and that under the line is the Denominator or whole number: Now decimal fractions are wrote without their denominators, for the integer or whole thing being always understood to confift of an unit with as many cyphers annex'd to the right hand, as the decimal fraction has places; and here the numerator or decimal itself is diftinguish'd from whole numbers by a feparating point ; thus, 5.4 is5; and 0.7 is; 35.05 is 35 , &c. But the different value of the feveral places will more plainly appear from the following Table. I Whole numbers. Decimal parts. 6 4 3 2 1.1 2 3 ~ Tens. Units place. Thoufands. Hundreds. Tens of Thoufands. Hundreds of Thoufands. Parts of Ten, or Parts of a Million. &c. From whence it is evident, that as whole numbers increafe by a tenfold proportion to wards wards the left hand; fo decimal parts decrease in the fame proportion towards the right. EXAMPLE. Write down or exprefs, fifteen parts of a hundred, in decimals. Answer .15 Again, Write down fifty two integers, and feventy five parts of one thoufand the integer. Answer 52.075 N.B. There are finite decimals, and those which are infinite. A finite decimal is that which ends at a certain number of places; but an infinite, that which no where ends, and thefe are called circulating decimals or repetends, and diftinguished by a dafh upon the figure, and are fuch wherein one or more figures are continually repeated; as if 3 was to be divided by 9, the quotient would be 3.3i the decimal being a continual circulation of 3's, equal to the fraction of 3. Thus 24.3666, &c. is call'd a fingle circulate, or repetend of 6's s and 6.264, &c. is call'd a compound circulating decimal, and has the firft and laft of the recurring digits dafhed accordingly. Otherwife any of thefe expreffions may be continued at pleafure, by repeating the circulating figure or figures without the dafh. In all operations, if the refult confifts of feveral nines in the decimal place, reject them, and make the next fuperior place an unit more; thus for 6.23999, &c. write 6.24. ADDITION B 2 H ADDITION and SUBTRACTION. CASE I. To add or fubtract finite decimals. AVING fet down all the propos'd numbers in their refpective places (as in addition, &c. of whole numbers) viz. every figure as well of the decimal parts as of the whole number directly underneatth thofe of the fame value or name, which may be very easily done if the feparating points are placed directly under one another. Then, add or fubftra&t them as if they were all whole numbers, and for their fum or difference, cut off by the feparating point, fo many places of decimal parts as there are in any of the given numbers. EXAMPLES in ADDITION. To add or fubtract decimals with fingle circu lates or repetends. RULE. Make every line to end at the fame place by filling up the vacancies with the recurring digits, and to the finite terms you may annex a cypher or cyphers, then add as before; only increase the fum of the right hand row with as many units as it contains nines, and the figure in the fum under that place will be a circulate. And for fubtraction, fill up and continue as in the following examples; and it the right hand of the fubtrahend be greater than the upper figure in the minuend, inftead of borrowing 10 as ufual, borrow 9 in this place, the reft as ufual, and the right hand figure of the remainder will be a circulate. 471.6418 15.2000 In thefe examples you obferve there are fingle recurring figures, which before you add or fubtract, must be made to end together. See the fame filled up. 3217.8460 8.1476 412.3822 16.6497 3707.8151 4.1736 395.6724 24.7 12.22 12.47 7.64333 Here it may be obferved, 2.7646 that in each Example the circulates are carried one 4.87873 place farther than the finite expreffions. MULTIPLICATION. CAS E I. When both the factors are finite decimals. RULE. WHETHER the factors, viz. the number propos'd to be multiplied together, are either all decimal parts, or decimals join'd to whole numbers, multiply them together as if they were all whole numbers; only obferve to point off fo many decimal places on the right hand of the product as are in both the multiplicand and multiplier. But when it fo happens that there are not fo many figures in the product as there are decimal places requir'd, "in that cafe you must fup ply |