REM.-When the repetend has the same figure repeated, a dot is placed over the single figure as above, .1 and 2; when the repetend has two or more figures, a dot is placed over the first and last; as .i2. 237 = 999) 237.000 (.237237, etc. = .237 999 1998 37 20 29 97 7230 6 993 237 Remainder the same as the first dividend; hence, the quotient will repeat. COR. 1.-A repetend is changed to a common fraction by placing under it, for a denominator, as many nines as there are figures in the repetend. COR. 2.-When the decimal fraction is partly a common decimal and partly a repetend, it is readily put in the form of a complex fraction, and then may be reduced accordingly; thus, REM.-Circulating decimals are seldom met with in practice, and the simplest manner to dispose of them is to reduce them to common fractions, and then use them as such. 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, 10 hundred = 1 thousand. 10 thousand = 1 ten-thousand. In the United States currency, the orders have the same relation; thus, 10 mills (m.) = 1 cent (ct.). 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 9.100 30.005 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 seven hundred and thirteen thousand, eight hundred and ninety-three mills; or, thus: Four thousand seven hundred and thirteen dollars, eighty-nine cents and three mills. REM. 2.-Mills are numerated the same as abstract numbers. SUBTRACTION. $287.304 1. From two hundred and eightyseven dollars, thirty cents and four mills, take one hundred and ninetyfour dollars, twenty-nine cents and 194.293 three mills. Remainder, Ninety-three dollars, one cent 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 |