Section 27. ADDITION OF DECIMALS. 1. Add together 5.018; 171.16; 88.133; 1113.6; .00456, and 14.178. Five and eighteen thousandths. One hundred seventy-one, sixteen hundredths. = Eighty-eight, and one hundred thirty-three thousandths. Write the numbers under each other according to their value, add as in whole numbers, and point off from the right hand as many places for decimals, as there are in that number, which contains the greatest number of decimals. 2. Add together 171.61111; 16.7101; .00007; 71.0006, and 1.167895. Ans. 260.489775. 3. Add together .16711; 1.766; 76111.1; 167.1, .000007, and 1476.1. Ans. 77756.233117. 4. Add together 151.01; 611111.01; 16.5; 6.7; 46.1, and .67896. Ans. 611331.99896. 5. Add fifty-six thousand and fourteen thousandths, nineteen and nineteen hundredths, fifty-seven and forty-eight ten thousandths, twenty-three thousand and five and four tenths, and fourteen millionths. Ans. 79081.608814. 6. What is the sum of forty-nine and one hundred and five ten thousandths, eighty-nine and one hundred seven thousandths, one hundred and twenty-seven millionths, forty-eight ten thousandths? Ans. 138.122427. 7. What is the sum of three and eighteen ten thousandths, one thousand five and twenty-three thousand forty-three millionths, eighty-seven and one hundred seven thousandths, forty-nine ten thousandths, and forty-seven thousand and three hundred nine hundred thousandths? Ans. 48095.139833. Section 28. SUBTRACTION OF DECIMALS. RULE. Let the numbers be so written, that the separatrix of the subtrahend be directly under that of the minuend; subtract as in whole numbers, and point off so many places for decimals, as there are in that number, which contains the greatest number of decimals.. 10. From seventy-three take seventy-three thousandths. Ans. 72.927. 11. From three hundred sixty-five take forty-seven ten thousandths. Ans. 364.9953. 12. From three hundred fifty-seven thousand take twenty-eight and four thousand nine ten millionths. Ans. 356971.9995991. Section 29. MULTIPLICATION OF DECIMALS. Multiply 18.72 by 7.1. Multiply 15.12 by .012. Multiply as in whole numbers, and point off as many figures for decimals in the product, as there are decimals in the multiplicand and multiplier; but, if there be not so many figures in the product, as in the multiplicand and multiplier, supply the defect by prefixing ciphers. Ans. .12649. Ans. 18.58922. Ans. .00000114. Ans. 1137. Ans. 2.20947. Ans. .00046967. Ans. 22.09. 3. Multiply 18.07 by .007. 4. Multiply 18.46 by 1.007. 5. Multiply .00076 by .0015. 6. Multiply 11.37 by 100. 7. Multiply 47.01 by .047. 8. Multiply .0701 by .0067. 9. Multiply 47. by .47. 10. Multiply eighty-seven thousandths by fifteen millionths. Ans. .000001305. 11. Multiply one hundred seven thousand and fifteen ten thousandths by one hundred seven ten thousandths. Ans. 1144.90001605. 12. Multiply ninety-seven ten thousandths by four hundred and sixty-seven hundredths. Ans. 3.886499. 13. Multiply ninety-six thousandths by ninety-six hundred thousandths. Ans. .0009216. Ans. 1. 14. Multiply one million by one millionth. 15. Multiply one hundred by fourteen ten thousandths. I Ans. .14. Section 30. DIVISION OF DECIMALS. 1. Divide $ 45,625 by 12.5. 2. Divide 45625 by 12. Divide as in whole numbers, and point off as many decimals in the quotient, as the number of decimals in the dividend exceed those of the divisor; but, if the number of those in the divisor exceed that of the dividend, supply the defect by annexing ciphers to the dividend. And, if the number of decimals in the quotient and divisor together are not equal to the number in the dividend, supply the defect by prefixing ciphers to the quotient. 15. Divide one hundred forty-seven and eight hundred twenty-eight thousandths by nine and seven tenths. Ans. 15.24. 16. Divide six hundred seventy-eight thousand seven hundred sixty-seven millionths by three hundred twentyeight thousandths. Ans. 2.069. Section 31. REDUCTION OF DECIMALS. I. To reduce a vulgar fraction to a decimal. 1. Reduce to a decimal. OPERATION. 8) 5.000 .625 That the decimal .625 is equal to §, may be shown by writing it in a vulgar fraction and reducing it thus, f = Ans. 625 NOTE. It is also evident, that .625 is equal to §, because the numerators have equal ratios to their denominators. Hence the following RULE. Divide the numerator by the denominator, annexing one or more ciphers to the numerator, and the quotient will be the decimal required. NOTE. It is not usually necessary, that decimals should be carried to more than six places. 2. Reduce to a decimal, 3. Reduce to a decimal. 4. What decimal fraction is equal to ? 5. Reduce to a decimal 6. Reduce to a decimal. Ans. .75. Ans. .875. Ans. .363636+. II. To reduce compound numbers to decimals. 7. Reduce 8s. 6d. 3qr. to the decimal of a £. |