DECIMALS Decimal parts of the dollar. 1. How many dimes equal a dollar? Then what part of a dollar is a dime? 2. How many cents equal a dollar? Then what part of a dollar is a cent ? 3. Ten mills equal one cent. How many mills equal a dollar? (Then what part of a dollar is a mill ?) Mills are not coined, but are used for exactness in computations. When we think of a dollar as dimes, it has 10 equal parts; when we think of a dollar as cents, it has 100 equal parts ; when we think of a dollar as mills, it has 1000 equal parts. A mill is 1o of a cent; a cent i of a dime; and a dime 1o of a dollar. This division of the dollar into tenths, hundredths, thousandths, etc., we caj decimal parts of the dollar. The decimal poinu is the point separating dollars and cents. Thus in $ 2.75 the ; joint separates 2 dollars from 75 cents. 4. What decimi part of a dollar are 5 dimes? 6 dimes ? 8 dimes? 9 dimes? 5. What decimal part of a dollar are 5 cents? 8 cents ? 9 cents? 10 cents ? The first place to the right of the decimal point is occupied by dimes or tenths of a dollar; the second place, by cents or hundredths of a dollar; the third place, by mills or thou sandths of a dollar. Since 8 dimes and 5 cents 85 cents, we generally say that cents occupy the first two places to the right of the decimal point. Observe that dimes, cents, and mills can always be written as decimal parts of a dollar; thus, 8 dimes = $.80; 2 mills $.002. 6. In $1.256, state what each figure represents. 7. Name the parts of a dollar, first as tenths, hundredths, and thousandths; then as cents and mills : $.65, $8.05, $2.005, $.50, $.75, $.80, $.705. 8. Write in figures: six dollars and five cents; ten dollars and fifty cents; three mills; five cents; five mills. We may also find tenths, hundredths, thousandths, etc., of any unit. READING AND WRITING DECIMALS One tenth may be written .1 as well as 1o; one hundredth may be written .01 as well as ido; and one thousandth may be written .001 as well as 1000 1. Read: .8 ft., .5 lb., .7 pk., .5 ft., .7 mi. A decimal fraction is any number of 10ths, 100ths, 1000ths, etc., of a unit. When expressed after a decimal point and without a written denominator it is usually called a decimal. The first place to the right of the decimal point is called tenths, the second place hundredths, and the third place thousandths. 2. In 55.55, the 5 hundredths is what part of the 5 tenths? the 5 tenths is what part of the 5 units? the 5 units is what part of the 5 tens? In any number, whether a whole number or a decimal, the value of a figure in any place is 1o of the value of the same figure standing one place to the left. 3. What is the largest decimal division of a unit? the second largest ? the third largest ? 4. .06= 10o = 1000 .9= = 1$ = 1šo = 1000 5. .25 = 100 = 1000 8. .025 = 1000 = 10000 6. .05= 100 = 1000 .349 = τοσο = τσόσο 7. 9. Observe that a decimal is always less than a unit. This number is read, five hundred twenty-five and two hundred fifty-six thousandths. 10. What do we call the decimal point when we read a number? What word, then, always joins the whole number and the decimal ? Observe that we express every number as units, or ones, and parts of a unit. Thus: 525 units and .256 of a unit. As the first decimal division of a unit is tenths, we always begin to enumerate the decimal at tenths' place; thus: tenths hundredths thousandths 5 11. At what place do we begin to enumerate whole numbers ? 12. Read the following: .25, .025, 25.005, 7.05, 321.1, 0.875, 1.008, 100.001, 0.001. 13. Write as decimals: Por ido, 136, 1o, 10 for 10009 261%, 1001000, 1187, 70,100 Write decimally: 15. Two and two thousandths. 16. Five hundredths. 17. Two hundred and two thousandths. COMPARISON OF COMMON FRACTIONS AND DECIMALS 1. * = 10% = 100%; .5=.50 =.500. 2. Do naughts at the right of a decimal affect its value? Annexing naughts to the right of a decimal does not affect its value. 3. What is a fractional unit? 4. What is the largest fractional unit that'may be expressed decimally? the second largest ? the third largest? 5. Change 6% to tenths. 6. Express .25, .45, .75, .025, each in the form of a common fraction. 7. Change .5 to equivalent decimals expressed in hundredths and thousandths. Thus .5 = .50 = .500. 8. Name the three largest fractional units in their order; the three largest fractional units expressed decimally. 9. Change 10% to an equivalent decimal. Changing a decimal to a common fraction. 1. Change .75 to a common fraction in its lowest terms. Expressed in the form of a common fraction .75 = 7= 18 = .75 = 136. By dividing both numerator and denomi nator of Ho by 25, we reduce it to its lowest terms, t. To change a decimal to a common fraction, write the decimal, omitting the decimal point, place the decimal denominator beneath it, and change the fraction to its lowest terms. Change to fractions : 8. .125 9. .425 10. Memorize the following equivalents : 1 =.5 or .50 } =.2 or .20 =.8 or .80 I=.25 = .4 or .40 š=.125 g=.375 31. .075 14. .625 20. .60 26. .48 32. .025 15. .75 21. 27. .150 33. .08 16. .65 22. .90 28. .50 34. .225 17. .375 23. .96 29. .025 35. .700 18. .80 24. .72 30. .08 36. .800 .125 |