9. How does the number of decimals in a product correspond to that of the factors? Ans. The number is equal. 10. How does the number of decimals in a dividend correspond to that of the divisor and quotient? Ans. It is equal. 11. If the divisor has more decimals than the dividend, what is necessary to be done? Ans. Add decimal zeros to the dividend until it has as many decimals as the divisor. 12. If the divisor and dividend have the same number of decimals, will there be any in the quotient? Ans. No. 13. If it be necessary that there should be decimals in the quotient, what must be done? Ans. More decimal zeros must be added to the dividend. 14. Do zeros annexed to a decimal change its value? Ans. No. 15. If zeros are prefixed to a decimal, and the decimal point removed to the left of the zeros, is the value changed? Ans. Each decimal zero thus prefixed renders the value one-tenth, or divides it by ten. 16. In multiplying by more than one figure, where is the first figure of each line or partial product placed, and why? Ans. It is placed in the column of the same order as the multiplier; that is, directly under it, because every consecutive order to the left is ten times the value of the preceding order. DENOMINATE NUMBERS. All arithmetical numbers may be considered Denominate, even abstract numbers, as every figure in each successive order, beginning at the right and going to the left, is ten times the value of the same figure in the previous order, and may be arranged in a table; thus, In the United States currency, the orders have the same relation; thus, Dimes and eagles are coins, but are not regarded in computation; but only dollars ($), cents, and mills, the cents holding two places. There is generally a decimal point placed between dollars and cents; thus, $456.295, which is numerated "four hundred and fifty-six dollars, twenty-nine cents and five mills. It may also be numerated without any change in its value, "four hundred and fifty-six thousand, two hundred and ninety-five mills. ADDITION. As the relations of the orders in United States money is the same as in abstract numbers, hence their application is the same; and in addition and subtraction like orders must be placed under each other, and in every other way the same methods are followed. $25.365 12.184 15.030 $91.684 PROBLEMS. 1. What is the sum of twenty-five dollars, thirty-six cents and five mills; twelve dollars, eighteen cents and four mills; nine dollars and ten cents; thirty dollars and five mills; fifteen dollars and three cents. Ans., Ninety-one dollars, sixty-eight cents and four mills. 2. Add the following sums of money: Five dollars, thirty cents and four mills. $5.304 REM. 1.-The sum of the last example may be numerated thus: Four millions eight hundred and thirteen thousand, eight hundred and ninety-three mills; or, thus: four thousand eight hundred and thirteen dollars, eighty-nine cents and three mills. REM. 2.-Mills are numerated the same as abstract numbers. $287.304 $93.011 three mills. and one mill. (2.) $475648.364 387654.875 SUBTRACTION. 1. From two hundred and eightyseven dollars, thirty cents and four mills, take one hundred and ninetyfour dollars, twenty-nine cents and Remainder, Ninety-three dollars, one cent $87993.489 (5.) REM.-As in addition and subtraction, so also in multiplication, the process is the same as that of abstract integers and decimals; hence there is no need of further exemplification. English money is reckoned in pounds, shillings, pence, and farthings; sometimes also in guineas; thus, Reduce £1 to shillings, pence, and farthings. As there are twenty shillings in one pound, there will always be twenty times as many shillings as pounds; and as there are twelve pence in every shilling, there will be twelve times as many pence as shillings; and four times as many farthings as pence. COR.-A higher denomination is reduced to a lower one by multiplication. Reduce 960 farthings to pence, shillings and pounds; thus, 4) 960 farthings. 12) 240 pence. 20) 20 shillings. 1 pound. As four farthings make one penny, there will be one |