28. 419863 and 23456 millionths. 30. 2986 and 298643 ten-millionths. 31. 3020 and 302 hundred-thousandths. 33. 8 thousand and 8 thousandths. 34. 645 million and 9 millionths. COMPARISON OF COMMON FRACTIONS AND DECIMALS ? ? 1. .5=5=100. .5=1000. 2. Then observe that 5 tenths = 50 hundredths 500 thousandths. .5 .50 = .500. = 3. 50 hundredths may be written .50, or .500. Does adding naughts to the right of a decimal change the value of the decimal? 4. What is the difference in value between $.5 and $.50? In writing decimal parts of a dollar, we always write two places for cents even if the last place is a naught. 5. Compare in value and 500 50 and 500 100 100 1000 6. Does canceling the same number of naughts from both numerator and denominator change the value of a fraction? 7. Since .5 .50.500, does canceling naughts from the right of a decimal change the value of the decimal? 8. Observe that canceling naughts from the right of a decimal really means canceling naughts from the numerator and the denominator. 9. .400 is read 400 thousandths. How else may it be read? 10. Is the unit in .4 the largest decimal unit in which .400 can be expressed? Read first as given, then as if the naughts at the right of the decimal were canceled : Changing decimals to common fractions. Write as common fractions and change to lowest terms: 9. Give the steps in changing a decimal to its fractional equivalent. A complex decimal is a decimal and a fraction united; thus, .16 is read 16 hundredths. 162 by 3 does not change the value of the fraction. 100 ADDITION AND SUBTRACTION OF DECIMALS 1. How must integers be written before they can be added? subtracted? 2. What change must be made in and before they can be added or subtracted? In adding or subtracting decimals, tenths must be placed under tenths, hundredths under hundredths, thousandths under thousandths, etc. Written Work 3. Add .8085 and .005. 4. Subtract .005 from .8085. Subtract examples 14 to 17 and add the remainders : 28. 12.015, 26.01102, 126.0592, 134.00876. 29. 100.001, 9.99, 149.0492, 7.077. 30. 2.2, 28.18, 140.027, 284.0295. 31. 318.003, 33.33, 495.0485, 12.0012. 32. Find the weight of four silver bars weighing as follows: 15.75 pounds, .125 pounds, 14.3125 pounds, and 16.875 pounds. 33. Find the number of acres in four fields containing, respectively, 4.125 acres, .3125 acres, 8.8 acres, and 9.85 acres. 34. Find the sum of one hundred twenty-five and seven hundredths, eighty-nine and two hundred thirty-five thousandths, one hundred twenty-seven ten-thousandths, and sixteen and four tenths. 35. A farm cost $4225.50; stock, $745.25; buildings, $1825.75; and implements, $358.45. What was the total cost? 36. How many square feet are there in four floors measuring, respectively, 245 square feet, 278 square feet, 174.375 square feet, and 168.3125 square feet? 53. (9.5-2.25)+(15.28–12.056)+(22.089–19.063). 54. (11.001-1.99)+(17.0107–14.014)+(29.3–23.2867). 55. The difference between two numbers is 1001.101, and the greater is 1101.011. What is the smaller number? 56. A is 35.875 years old, B is 48.25 years old, and C's age is 25.5 years less than the age of A and B combined. How old is C? 57. To the sum of .808 and 80.8 add their difference. MULTIPLICATION OF DECIMALS 1. Multiply .05 by .5. 2. What is the numerator in .05? in .5? 3. What is the denominator in .05? in .5? What shows the denominator in a decimal ? 4. Multiply the numerators in .5 x .05; thus, 5 x 5 = 25. 5. Multiply the denominators in .5 x .05; thus, 10 × 100 = 1000. 6. Write the result as a common fraction; thus, 25. |