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Express decimally: 35. 63

100

36. 116 37. 3100 38. 80010

39. 1318.
40. 770 2013
41. 3.9.2

1000 •
42. 700178867

a

common

ART. 169.-Changing Decimals to Common Frac

tions and Common Fractions to Decimals. 1. Change .84 to a common fraction of equivalent value. Process.

Analysis. —.84 written as

fraction is 80, which changed to its lowest .84 = 34=

terms is 2. ART. 170.—Rule for changing a decimal to a common fraction of equivalent value.- Write the denominator under the decimal, omit the decimal point, and change the fraction to its lowest terms.

Change the following to equivalent common fractions : 2. .8 8. 18.0205

14. 13.305 3. .06 9. 5.0025

15. 201.08 4. .25 10. 17.17

16. 93.003 5. .0125 11. 32.064

17. 11.9 6. 4.28 12. .185

18. 30.06 7. 13.075 13. 78.16

19. 109.008

1. Change š to an equivalent decimal.

Analysis. - = 3888, Process.

which changed to

thousandths is 3760 = 3888 ; 3808 f= 30 = .375.

This

expressed deciOr, thus, 8)3.000 •375

mally is .375.

ART. 171.-Rule for changing a common fraction to a decimal of equivalent value.-Annex ciphers to the numerator, divide by the denominator, and point off as many decimal places as there are ciphers annexed.

Change the following to equivalent decimals : 2. .

NOTE.-If, after annexing ciphers, the numerator is not exactly đivisible by the denominator, the decimal may be completed by writing the remainder as a common fraction, or the sign + may be added to the quotient to show that the division is not exact. Thus, š= .666+.

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25

9. 111

15. .331
4.
10. 74.3.

16. 61.23
5. 48
11. 101.15.

17. .7110
6. 164.
12. 4123.

18. 9.034
7. 18.
13. .427.

19. 6.64
8. To
14. 101 10.1..

20. 503.0577 21. Write a proper fraction and change it to a decimal of equivalent value.

22. Write a mixed number and change to a mixed decimal.

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Addition of Decimals.

ART. 172.–1. What is the sum of þy and i'? Of .5 and .3?

2. What is the sum of 10% and 24 ? Of .18 and .22 ? 3. What is the sum of 3 and 18? Of .4 and .32? 4. What is the sum of 3 and 10? Of .8 and .016 ? 5. What is the sum of .3, .15 and .004 ?

WRITTEN EXERCISES.

1. What is the sum of .12, 34.8, 7.004 ? Process.

.12 34.8 7.004

Analysis.- We write the numbers so that units of the same order stand in the same column, and add as in whole numbers.

41.924

ART. 173.Rule for Addition of Decimals.— Write the numbers so that units of the same order shall stand in the same column, and add as in whole numbers.

What is the sum of : 2. 765.789, 34.908, 65.8, 1001.0897 ? 3. 9.675, 35.6789, 80.6784, .80907 ? 4. .235, 27.6542, .0007, 6000.0872, 754.0001 ? 5. 1001.987, 10001.432, 5478, 9009, 5437, 9004?

6. Seventeen and seventeen thousandths, one thousand ten and one hundred eleven ten-thousandths, fifteen and seventy-five hundred-thousandths, one million and one millionth ?

7. Ten thousand ten and one hundred one hundredthousandths, five hundred fifty-five and eight hundred eighteen millionths, three hundred eighty-four thousand and six hundred-thousandths.

8. Twenty-seven and four thousand four hundred-thousandths, ten thousand ten and nineteen millionths, sixtyfour thousand and seventeen ten-thousandths ?

9. Seven hundred seven and four hundred thirteen thousandths, nine hundred nine and nineteen hundreths, four tenths, three thousand three and eleven thousandths.

10. What is the sum of 10 dollars 4 cents, 28 dollars

27 cents, 47 dollars 5 mills, 17 dollars ry cents, 101 dol. lars 1 mill, 34 dollars, and to of a dollar ?

11. Mr. A paid the following bills : groceries, $17.80 ; shoes, $23.42; milk, $3.75; clothing, $37.48; fuel, $19.50 : how much did he pay ?

12. A man paid $154.75 for a horse, $19.48 for a cow, $195.40 for a pair of mules, and $3.75 for a dog : what did he pay for all ?

13. A farmer sold some land for $524.50, hay for $21.38, oats for $17.75, wheat for $21.16, and corn for $19.20 : how much did he receive ?

14. Find the sum of 1,010 dollars 20 cents, 9 dollars 9 mills, 1 dollar 40 cents, 30 dollars 8 cents, 75 cents, and 17 dollars 1 mill.

15. A clerk's expenses for one month were : board, $24.40; washing, $3.25 ; gifts, $7.10; incidentals, $3.21 : what was the total ?

16. Illustrate by an original problem addition of decimals.

Subtraction of Decimals. ART. 174.-1. From to take io. From .8 take .%. 2. From To take 18o. From .17 take .01. 3. From To take tuo. From .043 take .023. 4. From 8 take lo. From 9 take .9. 5. From 24 take .18. From .35 take .02.

WRITTEN EXERCISES.

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1. From 21.304 take 17.017. Process.

Analysis. We write the numbers that 21.304

units of the same order stand in the same 17.017

column, and subtract as in whole numbers, 4.287

ART. 175.-Rule for Subtraction of Decimals.--Write the subtrahend under the minuend, so that units of the same order shall stand in the same column, and subtract as in whole numbers. If there are more decimal places in the subtrahend than in the minuend, fill the vacant orders of the minuend with ciphers.

Find the difference between
2. 203.456 and 199.009.
3. 89.076 and 64.0009.
4. 3003.765 and 2101.1001.
5. 90.678954 and 1001.0077.
6. 78786.0008 and 9999.090909.
17..y and my ten-millionths.

8. 4 and 14 hundred-thousandths and 2 and 22 millionths.

9. 5 hundredths and 5 millionths. 10. From 33 dollars 5 cents take 21 dollars 6 mills. 11. From 113 dollars mills take 101 dollars 8 cents.

12. From 19 dollars 20 cents take 11 dollars 18 cents 1 mill.

13. A clerk's income was $1,235.60 and his expenses $750.23: how much did he save ?

14. A man handed his grocer a twenty-dollar bill in payment for a debt of $17.60 : how much change did he receive ?

15. Illustrate by an original problem subtraction of decimals.

Multiplication of Decimals. ART. 176.-1. What is the product of 17 x 5 ? Of 1 x 5? Of .2 x 4 ?

2. What is the product of ndo x7 ? Of .03 X.6?

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