Note. If there be one figure in the decimal, it is so many tenths; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c. NUMERATION OF DECIMAL FRACTIONS. Let the pupil write the following numbers. 1. Three hundred seven, twenty-five hundredths. 2. Forty-seven, and seven tenths. 3. Eighteen and five hundredths. 4. Twenty-nine and three thousandths. 5. Forty-nine ten thousandths. 6. Eight and eight millionths. 7. Seventy-five and nine tenths. 8. Two thousand and two thousandths. 9. Eighteen and eighteen thousandths. 10. Five hundred five, and one thousand six millionths. Section 27. ADDITION OF DECIMALS. 1. Add together 5.018; 171,16; 88.133; 1113.6 ; .00456, and 14.178. OPERATION. 5.018 =Five and eighteen thousandths. 171.16 = One hundred seventy-one, sixteen hundredths. 88.1 33 Eighty-eight, and one hundred thirty-three thousandths, 111 3.6 = One thousand one hundred thirteen, and six tenths. = Fourteen, and one hundred seventy-eight thousandths. 139 2.0 935 6 = One thousand three hundred ninety-two, and nine thousand three hundred fifty-six hundred thousandths. RULE. 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. J 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, that is, units under units, and tens under tens, fc.; 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. OPERATION. 1. 3. 2. 47.1 17 1 1.078 9.8 1 8.78195 46.13 4. 1.1 1986 1.2 68 38.3 35 0 5 33 2385 85.98714 15.12 5. From 81.35 take 11.678956. Ans. 69.671044. 6. From 1. take .876543. Ans. ,123457. ny. From 100. take 99.111176. Ans. .888824. 8. From-87.1 take 5.6789. Ans. 81.4211. 9. From 100. take .001. Ans. 99.999. 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 twentyeight and four thousand nine ten millionths. Ans. 356971.9995991. 13. From .875 take .4. Ans. .475. 14. From .3125 take .125. Ans. .1875. 15. From .95 take .44. Ans. .51. 16. From 3.7 take 1.8. Ans. 1.9. 17. From 8.125 take 2.6875. Ans. 5.4375. 18. From 9.375 take 1.5. Ans. 7.875. 19. From .666 take .041. Ans. .625. 18.7 2 181% = 1072 7.1 =71 18073 X H= 113812=13291% Ans. 2. Multiply 15.12 by .012. Ans. .18144. OPERATION BY DECIMALS. BY VULGAR FRACTIONS. 1514% = 1542 .012 30 24 1512 J8144 Ans. .012 = τόσο 180102 x ango 18 144. Ans TO0000 Hence, we deduce the following RULE. Multiply as in whole numbers, and point of 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. .00000 1305. 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. 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. 17. 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. |