Hence, we deduce the following RULE. 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. 3. Multiply 18.07 by .007. Ans..12649. 4. Multiply 18.46 by 1.007. Ans. 18.58922. 5. Multiply .00076 by .0015. Ans. .00000114. 6. Multiply 11.37 by 100. Ans. 1137. 7. Multiply 47.01 by .047. Ans. 2.20947. 8. Multiply .0701 by. 0067. Ans. .00046967. 9. Multiply 47. by .47. Ans. 22.09. 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. .00009216. 14. Multiply one million by one millionth. Ans. 1. 15. Multiply one hundred by fourteen ten thousandths. Ans. .14. 16. Multiply one hundred and one thousandth by ten thousand one hundred one hundred thousandths. Ans. .01020201. 17. Multiply one thousand fifty and seven ten thousandths, by three hundred five hundred thousandths. Ans. 3.202502135. 18. Multiply two million by seven tenths. Ans. 1400000. 19. Multiply four hundred and four thousandths by thirty and three hundredths. Ans. 12012.12012. 20. What cost 46lbs tea at $ 1.125 per lb. ? $ 51.75. 21. What cost 17.125 tons of hay at $ 18.875 per ton ? Ans. $ 323.234375. 22. What cost 18lbs. sugar at $.125 per lb. ? Ans. $ 2.25. Section 30. DIVISION OF DECIMALS. 1. Divide $ 45.625 by 12.5. 2. Divide 4502 by 12 fo. OPERATION BY DECIMALS. BY VULGAR FRACTIONS. . 12.5) 45,6 25 (3.65 45 62 = 45062 375 123 = 185. 4.82 X 125=+*$388=318 Ans. Hence the following RULE. 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, reduce the dividend to the same denomination as the divisor by annexing ciphers. 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. 3. Divide 183.375 by 489. Ans. .375. 4. Divide 67.8632 by 32.8. Ans. 2.069. 5. Divide 67.56785 by .035. Ans. 1930.51. 6. Divide .567891 by 8.2. Ans. .069255. 7. Divide .1728 by 12. Ans. .0144. 8. Divide 172.8 by 1.2. Ans. 9. Divide 1728. by .12. Ans. 10. Divide .1728 by .12. Ans. 11. Divide 1.728 by 12. Ans, 12. Divide 17.28 by 1.2. Ans. 13. Divide 1728 by .0012. Ans. 14. Divide .001728 by 12. Ans. 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. That the decimal .625 is equal to , 8) 5.000 may be shown by writing it in a vulgar .6 2 5 fraction and reducing it thus, *3= Ans. OPERATION. 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. Reduced to a decimal. Ans. .75. 3. Reduce ž to a decimal. Ans. .875. 4. What decimal fraction is equal to jo? Ans. .4375. 5. Reduce A to a decimal. Ans. .363636 + 6. Reduce is to a decimal. Ans. .416666 +. II. Reduce compound numbers to decimals. 7. Reduce 8s. 6d. 3qr. to the decimal of a £. OPERATION. 43.00 1 2 6.75 2018.5 6 2 5 .4 2812 5 The 3 farthings are į of a penny, and these, reduced to decimals, are .75 of a penny, which we annex to the pence, and proceed in the same manner with the other terms. Hence the following RULE. Write the given numbers perpendicularly under each other for dividends, proceeding orderly from the least to the greatest ; opposite to each dividend on the left hand, place such a number for a divisor, as will bring it to the next superior name, and draw a line between them. Begin at the highest, and write the quotient of each division, as decimal parts, on the right of the dividend next below it, and so on, until they are all divided ; and the last quotient will be the decimal required. 8. Reduce 158. 6d. to the fraction of a £. Ans. .775. 9. Reduce 5cwt. 2qr. 14lb. to the decimal of a ton. Ans. .28125. 10. Reduce 3qr. 2llb. to the decimal of a cwt. Ans. .9375. 11. Reduce 6fur. 8rd, to the decimal of a mile. Ans. .775. 12. Reduce 3R. 19p. 167ft. 72in. to the decimal of an Ans. .872595 +. Note 1. If it be required to reduce pounds, shillings, pence, and farthings, of the old New England currency, to dollars, cents, and mills ; the pounds, shillings, &c. may be reduced to the decimal of a £; and if this decimal be multiplied by 10 and the product divided by 3, the quotient will be dollars and cents. But if the above deci. mal be multiplied by 10, and the product be divided by 4, the quotient will be the reduction of the old currency of New York to dollars and cents. Note 2. If it be required to bring English sterling money to dollars and cents, let the pounds, &c. be reduced to the decimal of a penny; then divide this decimal by , and the quotient is dollars and cents. 13. Change 18£. 158. 6d. of the old New England currency, to dollars and cents. acre. OPERATION. 18£. 15s. 6d.= 18.775£.; 18.775 X 10 = $ 62.581 Ans. 14. Change 15£. 15s. 9d. of the old currency of New York, to dollars and cents. OPERATION. 15£. 15s. 9d.= 15.7875 £.; 15.7875xY=$39.46.84 Ans. 15. Change 176£. 193. 9d. sterling to United States currency. Ans. $ 786.61 +. OPERATION. 176£. 19s. 9d. =176.9875£.; 176.9876x2=$ 786.61 +. III. To find the value of any given decimal in the terms of the integer. 16. What is the value of .9875£. ? Ans. 19s. 9d. OPERATION. .9875 This question is performed by 20 the same principle we adopted 19.75 00 in finding the value of a vulgar 12 fraction in the known parts of the 9.0 000 integer. Hence the following RULE. Multiply the given decimal by that number which it takes of the next denomination to make one of that greater, and cut off as many places for a REMAINDER, on the right hand, as there are places in the given decimal. Multiply the REMAINDER by the next lower denomination, and cut off for a remainder as before, and so proceed, until the decimal is reduced to the denomination required; the several denominations standing at the left hand are the answers required. 1. What is the value of .628125 of a £ ? Ans. 12s. 6 d. 2. What is the value of .778125 of a ton ? Ans. 15cwt. 2qr. 7lb. 3. What is the value of 75 of an ell English ? Ans. 3qr. 3na. |