3. Four hundredths. 42 hundredths.
4. 125 thousandths. 22 thousandths.
5. 20 hundredths. Eight thousandths.
6. 30 thousandths. 206 thousandths.
7. 3027 ten-thousandths.

8. Three hundred ten-thousandths.
9. Forty-two ten-thousandths.
10. 145 hundred-thousandths.
11. Fifty-one hundred-thousandths.
12. One hundred seven millionths.

13. 306 ten-millionths.

14. 3259 hundred-thousandths.

15. 429 ten-millionths.

16. 4268 hundred millionths.

17. 13,760 millionths.

18. Three hundred forty-two millionths.

19. One hundred forty-five hundred thousandths.
20. 703,205 millionths.

4. Express as mixed decimals the following:

1. Read $12.925 as a mixed decimal, and as dollars, cents, and mills.

It is read "12 and 925-thousandths dollars," or "12 dollars, ninety-two cents, five mills."

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3. Express decimally $48, $201, $351, $180, $11%,

84

ΤΟ

839

$33100, $1000, $135, $645, $33,AL, $68, $1860, $1000 $6100, $68,3%, five cents, five dimes, five mills, five dollars five cents five mills.

REDUCTION.

To Like Decimals.

$180 = $1880. Therefore $.06 = $.060.

PRINCIPLE.

Annexing ciphers to a decimal does not alter its value.

EXERCISES.

1. Reduce .7, .05, and .304 to like fractions.

Process.

.7= .700 .05.050

.304.304

Explanation.

Since

Thousandths is the lowest order given, hence all the fractions must be reduced to thousandths. annexing ciphers to a decimal does not alter its value, we annex two ciphers to .7, thus rendering it 700

thousandths; one cipher to .05, thus rendering it 50 thousandths.

RULE.

By annexing ciphers give each decimal the same number

of decimal places.

2. Reduce to like decimals the following:

1. .25, .025, .37.

2. .523, 4.36, 5.0315.

3. .4036, .5, .375,

4. .06, .008, .4267, .026.

5. .409, 3.61, .75, .10055, 19.6.
6. 7.07, 5.0909, 1.9090, 19.099.
7. .12, .8, 306.973, .004, 48.56.
8. .0436, .04506, .82.

9. .8104, .0008, 8000.4.
10. 8.1, .43, .68, 3.96.

To a Common Fraction.

1. What is the denominator of .125?

2. What is its numerator?

3. Write .125 as a common fraction.

4. What part of the expression .125 did you

EXERCISES.

1. Reduce .375 to a common fraction.

Process.

omit?

Write the decimal, omitting the decimal point; supply the decimal denominator, and reduce the fraction to its lowest terms.

2. Reduce the following decimals according to the rule:

COMPLEX DECIMALS.

EXERCISES.

1. Reduce .9 to a common fraction.

Process.

Explanation.

.93 = ff = 38 = 14 Multiplying both terms of by 3, we

obtain 38.

1. What is the denominator of a common fraction that may be directly expressed as a decimal?

2. If be reduced to a decimal, what is the smallest

5. How does the number of places in the quotients agree

with the number of ciphers annexed?

EXERCISES.

1. Reduce to a decimal.

Process.

3.000 = .375

Explanation.

We find by trial that three ciphers must be annexed to 3 to secure a complete quotient. The three

ciphers annexed require the pointing off of three decimal places in the quotient.

RULE.

Annex ciphers to the numerator and divide by the denominator. Point off in the quotient as many decimal places as there are ciphers annexed.

2. Reduce the following to decimals:

NOTE. It is not

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possible in every case to render the division exact by annexing ciphers. Frequently a remainder occurs, which may be used as the numerator of a fraction; or it may be disregarded, and the sign + employed to denote the incompleteness.