From the foregoing we have the following: To Write Decimals a. Fix the decimal point. b. Write the figures so that as many places are occupied at the right of the decimal point as the decimal requires. NOTE. In case there are not enough figures to occupy all of the places of the decimals, ciphers must be prefixed to fill up the vacant orders. Write the following in figures: 1. Nine-tenths. 2. Six-tenths. 3. Four hundredths. 4. Twenty-seven hundredths. 6. Three thousandths. 7. Two hundred sixty-nine thousandths. 8. Two hundred, and sixty-nine thousandths. 9. Two hundred sixty, and nine thousandths. 10. Eight ten-thousandths. 11. Forty-one ten-thousandths. 12. Forty, and one ten-thousandth. 13. Six hundred thirty-four ten-thousandths. 14. Six hundred, and thirty-four ten-thousandths. 15. Six hundred thirty, and four ten-thousandths. 16. Three thousand four ten-thousandths. 17. Nine thousand, and six ten-thousandths. 18. Sixteen hundred thousandths. 19. Eighty-two hundred-thousandths. 20. Eighty, and two hundred thousandths. To Read Decimals Read the decimal as a whole number, and then add the name of the right hand order of the decimal. How many figures are required to express, 1. Tenths? 3. Thousandths? 5. Millionths? 2. Ten-thousandths? 4. Hundredths? 6. Hundred-thousandths? What is the name of the decimal expressed by 7. Two figures? 8. Four figures? 9. One figure? 11. Six figures? 12. Five figures? 116. Reduction of Decimals consists in changing their form without altering their value. 117. To reduce a common fraction to a decimal. 1. Reduce to a decimal. We therefore have the following rule: To Reduce a Common Fraction to a Decimal a. Annex ciphers to the numerator and divide by the denomi nator. b. Point off as many decimal places in the result as there are ciphers annexed to the numerator. NOTE. If there continues to be a remainder and the division will not end, the result is called a repeating decimal, and the number repeated is called a repetend. 14. Reduce 42 to a mixed decimal. 15. Reduce 200ʊ to a mixed decimal. 118. To reduce a decimal to a common fraction. 1. Reduce .25 to a common fraction. To Reduce Decimals to Common Fractions a. Omit the decimal point, and express the denominator of the fraction. b. Reduce the fraction to its lowest terms. 2. Reduce .5 to a common fraction. 3. Reduce .45 to a common fraction. 4. Reduce .125 to a common fraction. 5. Reduce .375 to a common fraction. 6. Reduce .016 to a common fraction. 7. Reduce .075 to a common fraction. 8. Reduce .625 to a common fraction. 9. Reduce .9375 to a common fraction. 10. Reduce .0008 to a common fraction. 11. Reduce 28.0625 to a mixed number. 12. Reduce 136.005 to a mixed number. 13. Reduce .44 to a common fraction. 14. Reduce .1428574 to a common fraction. 15. Reduce .0833 to a common fraction. 16. Reduce .0053 to an equivalent common fraction. 17. Reduce 107.1663 to an equivalent mixed number. 18. Reduce 8.123 to an equivalent mixed number. 19. What mixed number is the equivalent of 16.04831? 20. What mixed number is the equivalent of 143.421? ADDITION OF DECIMALS 119. 1. Find the sum of 13.25, .637, 142.6, .085 and 4.2631. SOLUTION 13.25 .637 142.6 .085 4.2631 260.8351 From the foregoing we have the following: To Add Decimals a. Write the numbers so that figures of the same order are in the same column, with the decimal points in a column. b. Add the same as in whole numbers and place the decimal point in the result directly under the decimal points above. Find the sum of each of the following: .853 + 7.28 = x .3284.3162 + .3426 + .2341.3456 +2.561 +17.928 + .785 .4234 +4213 + 5.207 + 21.15 x + x + x + 7. 21.75, 8.9, 148.273 and 269.412. 8. 328.013, 93.6, 80.003 and 964.24. = x + .095 = x + x = 11. 1260.9, 5394.08, 675.149 and 260.024. 12. Add thirty-seven, and three hundredths; five hundred twenty-one thousandths; nine-tenths; one thousand; four thousand, and four ten-thousandths. 13. What is the sum of twenty-six, and twenty-six hundredths; seven-tenths; six, and eighty-three thousandths; four, and four-thousandths? 14. What is the sum of twenty-eight, and seven-tenths; one hundred forty, and sixteen thousandths; thirty-seven ten-thousandths; twenty-five, and fifteen hundred-thousandths; four, and eight hundredths? 15. How many yards in four pieces of cloth, the first containing 28.375 yards; the second 26.4635 yards; the third 14.05 yards, and the fourth 18.2 yards? 16. A boy paid $8.40 for a coat, $3.65 for a vest, $6.152 for a pair of pants, $4 for a hat and $2.857 for a pair of shoes. What sum did he pay for all? 17. A farmer received $478.285 for wheat, $362.675 for oats, $140 for rye, $360.90 for corn and $200 for barley. did he receive for all? 18. My farm consists of 7 fields, containing 12 acres, 9 acres, 241 acres, 41% acres, 8% acres, and 15 spectively. How many acres in my farm? How much acres, 18 acres re NOTE. Reduce the common fractions to decimals before adding. 19. A farmer sold 84 bushels of wheat; 136 bushels of oats; 122 bushels rye; 29.0687 bushels of barley; and 548.365 bushels of corn. How many bushels of grain did he sell in all? 20. A merchant sold 3 yards of cloth for $4.675; 2.5 yards of another piece for $13; 113 yards of another piece for $63; and 5 yards of another piece for $15. How many yards did he sell in all, and for how much? 21. Three hundred four, and thirty-two thousandths miles; eighteen, and two thousand seventy-five hundred-thousandths miles; three, and fifteen ten-thousandths miles; and five thousand eighty-two, and one thousand nineteen hundred-thousandths miles equal what? 22. A farmer owns five tracts of land containing respectively eight hundred seventy-six, and eighteen thousandths acres; twenty-eight, and seven-tenths acres; four hundred fifty-six, and five hundred six ten-thousandths acres; seventy-two, and thirteen thousandths acres; and nine thousand three hundred twenty-four, and seven hundred sixteen hundred-thousandths acres. How many acres of land did the farmer own? |