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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 dol

lar? Then what part of a dollar is a cent?

3. Ten mills equal one cent. dollar? (Then what part of a dollar is a mill?) How many mills equal a

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 of a cent; a cent of a dime; and a dime of a dollar.

This division of the dollar into tenths, hundredths, thousandths, etc., we cal decimal parts of the dollar.

The decimal point is the point separating dollars and cents. Thus in $2.75 the point separates 2 dollars from 75 cents.

4. What decima 8 dimes? 9 dimes?

5. What decimal 9 cents? 10 cents?

l part of a dollar are 5 dimes? 6 dimes?

part of a dollar are 5 cents? 8 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 thousandths of a dollar.

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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.

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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 one hundredth may be written .01 as well as ; 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 point is a period placed before tenths.

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

figure standing one place to the left.

of the value of the same

3. What is the largest decimal division of a unit? the second largest? the third largest?

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Observe that a decimal is always less than a unit.

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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:

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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: 6, 10, 1800, 10, 1880, 1000, 261000, 1001000, 180, 70-105.

Write decimally:

14. Two thousandths.

15. Two and two thousandths.

16. Five hundredths.

17. Two hundred and two thousandths.

18. Two hundred two thousandths.

19. Three and five tenths.

20. Seventy-five hundredths.

21. Five hundred and five thousandths.

22. Thirty-three thousandths.

23. Ninety-five thousandths.

24. Two hundred and five hundredths.

25. Six and nine tenths.

26. Six hundred and six hundredths.

COMPARISON OF COMMON FRACTIONS AND DECIMALS

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1. 10=100=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 to tenths.

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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.

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8. Name the three largest fractional units in their order; the three largest fractional units expressed decimally.

9. Change 125 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 .75.75%. By dividing both numerator and denominator of 75% by 25, we reduce it to its lowest terms, §.

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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.

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