ART. 169.-Changing Decimals to Common Fractions and Common Fractions to Decimals. 1. Change .84 to a common fraction of equivalent value. Process. .8484. 100 Analysis..84 written as a common fraction is, which changed to its lowest terms is . 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. 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. 3. NOTE.-If, after annexing ciphers, the numerator is not exactly divisible 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, = .666+. 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. Addition of Decimals. ART. 172.—1. What is the sum of and? Of .5 and .3? 2. What is the sum of 1 and 24? Of .18 and .22? 6 and 18? Of .4 and .32? and? 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 41.924 Analysis. We write the numbers so that units of the same order stand in the same column, and add as in whole numbers. 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 7 cents, 101 dollars 1 mill, 3 dollars, and 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 take. From .8 take .7. 2. From 18 take 3. 3. From From .17 take .01. take. From .043 take .023. 4. From 8 take f. From 9 take .9. 5. From .24 take .18. From .35 take .02. WRITTEN EXERCISES. 1. From 21.304 take 17.017. Process. 21.304 17.017 Analysis. We write the numbers SO that units of the same order stand in the same column, and subtract as in whole numbers. 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. 7. .7 and 7 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 7 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 × 5? Of × 5? Of .2 × 4? 2. What is the product of 10 × 7? Of .03 x .6? |