13. What is the decimal expression for 5 cents? Ans. Sign, point, naught, five; read five hundredths ($.05). 14. Express decimally 7 cents; 9 cents; 15 cents. 15. Express decimally 7 mills; 5 cents 6 mills. 16. Express decimally 2 dollars 45 cents and 6 mills. Ans. Sign, two, point, four, five, six; read, two and four hundred fifty-six thousandths dollars ($2.456). 17. What is the decimal expression for 84 cents 5 mills? 18. Change .3 to hundredths; to thousandths. 19. Change .4 and .05 to thousandths; .07 and .01 20. Change .5, .08, and .023 to equivalent decimals, having a common denominator of 1000. Also, .14, .009, and .6. .7, .007, and .091. 21. Reduce .7, .150 and .600, to equivalent decimals, having the least common denominator. Also, .50, .250, and .1700. .43, .006, and .0214. 280. From the foregoing it appears, 1. That dollars may be reduced to cents by annexing two ciphers; and to mills, by annexing three ciphers. Omit the sign $ and write cts. or m. after the result. 2. That cents may be reduced to mills by annexing one cipher. 3. That cents may be reduced to dollars by pointing off two figures from the right; and mills to dollars, by pointing off three figures from the right, and prefixing the sign ($). 4. That mills may be reduced to cents by pointing off one figure from the right. 5. That two or more decimals are reduced to a common denominator by annexing or rejecting ciphers at the right until the decimal places of all are equal. WRITTEN 281. Reduce EXERCISES. 1. $85 to cents. (280, 1.)| 5. $57 to mills. 2. $615 to cents. 3. $24.06 to cents. 4. $9.206 to mills. Change 6. 86 cents to mills. (280, 2.) 7. $.763 to mills. 8. $.47 to mills. 9. 486 cts. to dollars. (280, 3.)| 12. 846 mills to cents. 10. 32462 cents to dollars. 11. 40327 mills to dollars. 13. 50000 mills to dollars. 14. 61040 cents to dollars. 15. Reduce .7, .05, and .304, each to hundred-thousandths. (280, 5.) 16. Reduce 2.5, .107, and .0008, each to ten-thousandths. 17. Change 4, 2.17, .136, and .0408 to equivalent decimals having a common denominator. 18. Reduce 9 tenths, 24 thousandths, 109 hundredthousandths, and 47 millionths to equivalent decimals having the least common denominator. Also, 19. 100.03, 41.0034, .475, .0753, and 6.00044. 20. .84003, 120.4, 5.00031, and 15.240007. 282. To reduce a decimal to a fraction. ORAL EXERCISES. 25 100 ? .6? 1. How many halves in? In? Ing? In In .75? ? In .20? Tenths? RULE.-Omit the decimal point, supply the proper denominator, and then reduce the fraction to its lowest terms. 14. Reduce .131 to an equivalent fraction. 16. $.624. 19. .58. 22. $.66. 25. .444$. 23. $.16. 26. .00081. 33. 38.41. 17. $.08. 20. .93. Express by an integer and a fraction, 27. $15.4. 29. $9.625. 31. 24.26. 28. $36.75. 30. $27.375. 32. 84.058. 34. 104.00. 284. To reduce a fraction to a decimal. ORAL EXERCISES. 1. How many tenths in ? How many hundredths? How many thousandths? 2. How many tenths in? Hundredths in ? In ? 3. How many hundredths in? In ? In ? sulting terms by 8, the significant figure of the denominator, to obtain the decimal denominator 1000. Then change to the decimal form. (253.) 2. Reduce to an equivalent decimal. II. Point off as many decimal places in the result as there are ciphers annexed. The sign is sometimes placed after the result to indicate that there is still a remainder. Thus, .666+, or .6663. Reduce to five decimal places: 286. 1. What is the sum of and? .6 and .4? 2. What is the sum of and 13? .11 and .15? 3. What is the sum of .12 and .20? .15 and .25? 4. Find the sum of 6 mills and 9 mills. .008 and .021. 5. What is the sum of 4 and .09? Of .04 and .009? How many decimal figures in the sum of tenths and tenths? Of tenths and hundredths? Of hundredths and thousandths? Of tenths and thousandths? In adding several decimals, each having a different number of decimal places, how many places will there be in the sum? 287. Since decimals and integers increase and decrease uniformly by the scale of ten, decimals expressing like parts of a unit may be added, subtracted, multiplied, and divided in the same manner as integers. The pupil should obtain and express all results in decimal form. 288. 1. Find the sum of 12.07, 326.2086, .768, and 1.9. OPERATION. 12.0700 326.2086 .7680 1.9000 340.9466 ANALYSIS.-Write the numbers so that units of the same order stand in the same column. After reducing the decimals to a common denominator by annexing ciphers (280, 5), or supposing them to be annexed, add as in integers, placing the decimal point before tenths ir the sum. In like manner find the sum 2. Of .375, .24, .536, .0437, .50039, and .008236. |