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. 51

15. 7370808800
2. 7 %
9. 27148

16. 41180
3. 818
10. 541176

17. 6455.
4. 9770
11. 7410800

18. 33140000
5. 121000
12. 86_3216

19. Tot 000

10000: 6. 1517%

4000 13. 48-21875

20.
100 000

10000
7. 15-406
14. 56143760

21. 957337600

95100000 1000

8. 24 208

.

.

100000

UNITED STATES MONEY.

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."

2. Read in like manner the following: 1. $89.06. 5. $59.375.

9. $1.375. 2. $94.254. 6. $86.017. 10. $0.876. 3. $69.015. 7. $314.002. 11. $0.093. 4. $195.005. 8. $20.25.

12. $0.001. 3. Express decimally $180, $20_, $351, $10, $145, $ 136, $64 %, $33200, $190864, $1847, $170, $683%, $68 33%, 13.5*010

, five cents, five dimes, five mills, five dollars five cents five mills.

41 10

83.9.

39

1000

1°,

REDUCTION.

To Like Decimals. $160 = $1680. 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.

Explanation. .7 = .700 Thousandths is the lowest order given, hence all .05 = .050

the fractions must be reduced to thousandths. Since

annexing ciphers to a decimal does not alter its value, 301 .304

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 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: 1. .45.

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 denominator it can have ?

3. = how many 10ths ?
4. How is $ written decimally? How $?

5. How does the number of places in the quotients agree with the number of ciphers annexed ?

=.375

8

1. 1

25. 372

23

3. §.

15

15

12. 4.

347

5

EXERCISES.
1. Reduce s to a decimal.
Process.

Explanation. 3.002

We find by trial that three ciphers must be an

nexed 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 :

9. 28 .
17. 14

1250;
2.
10.
18. 3.

26. do
11. . 19. 12.

27.

1280 4. Z.

20. 11. 28.

2560
5.
13. 16

21. 51. 29. Todoo
22. 486

15625
7. H.
15. 7

31. 31895
:

32 76 •
8. 32.
16.
24. sto

81920 Note. - It is not 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. 3. Reduce to a decimal.

Process.

3. ogle = .4285%, or .4285 +.
4. Reduce to decimals the following:

6.
. Út

7. 9. 12. .
3. Bg 8.

13. 9. 15.

1728 15. 34.

20. 1898.

6. 16

14. 3

201
2 56

30. 34 76

17

23. 12392

32. 3856

=

5

11. .

1. } 2. 5.

6

16. t. 17. To 18. Ito

14. 47.

19. 307

74