24. 25. 26. 27. 1.5.7 Ans. 440. Ans. .01 Ans. 10. Ans. 1000. Ans. .0265625 Ans. .001 Ans. .000001 Ans. 1. Divide 1 thousandth by 1 thousandth. 1 ten-thousandth 1 ten-millionth. Ans. 1000. 1 hundredth÷4 millionths. Ans. 2500. Ans. 2.142857+ ART. 184. To divide a Decimal by 10, 100, 1000, &c., remove the decimal point as many places to the left as there are ciphers in the divisor : And, if there are not so many figures on the left of the point, supply the deficiency by prefixing ciphers. ART. 185. REDUCTION OF DECIMALS. CASE I.-To reduce a common fraction to a decimal. 1. Reduce the fraction to a decimal. SOL. The numerator, 3, will not be changed by writing ciphers in the place of tenths, hundredths, &c. Since a fraction is expressed in the form of an unexecuted division (Art. 125), regard the operation as division of decimals, and perform it according to the rule, (Art. 183). Since the divisor has no decimal places, the quotient must have as many places as there are ciphers annexed. *2. Reduce to a decimal. OPERATION. 4)3.00 Ans. .75 Ans. .125 Rule for Case I.-Annex ciphers to the numerator, divide by the denominator, and point off in the quotient as many places for decimals as there are ciphers annexed to the numerator. NOTE. When common fractions can not be exactly expressed in decimals, continue to divide till the quotient is sufficiently exact. ART. 186. To reduce a decimal to a common fraction, and to its lowest terms. 1. Reduce .75 to a common fraction in its lowest terms. SOL.-By writing the denominator, .75 becomes 15, and, reduced to its lowest 100' terms by the rule (Art. 138), it becomes OPERATION. .75=75 Ans. του *2. Reduce .6 to a common fraction, in its lowest terms. Ans. . Rule for Case II.- Write the denominator under the decimal; it will then be a common fraction, which reduce to its lowest terms, (Art. 138). REDUCE TO COMMON FRACTIONS, IN THEIR LOWEST TERMS, 24 NOTE. When a decimal contains several places of figures, their value can be found nearly by inspection. To do this, take the first or the first two figures, as the numerator, of which 10 or 100 is the denominator, then reduce it to its lowest terms: Thus .332125 is nearly 1 third; .258321 is nearly 1 fourth. CASE III. ART. 187. To reduce a decimal of one denomination to an equivalent decimal of another denomination. 1. Reduce .25 qt. to the fraction of a pt. SOLUTION. To reduce quarts to pints, we multiply by 2, the number of pints in a quart. Therefore, multiply the fraction of a quart by 2, to reduce it to the fraction of a pint. Art. 81. 2. Reduce .5pt to the fraction of a qt. SOLUTION. To reduce pints to quarts, we divide by 2, the number of pints in a quart. Therefore, divide the fraction of a pint by 2, to reduce it to the fraction of a quart. Art. 81. OPERATION. qt. .25 2 .50 Ans. .5 pt. OPERATION. pt. 2).5 Ans. .25.qt. *3. Reduce .125 bu. to the fraction of a pk. Ans. .5 *4. Reduce .7pk. to the fraction of a bu. Ans. .175 Rule for Case III.-Multiply or divide as in Reduction of Whole Numbers, Art. 81, according to the rules for the Multiplication and Division of Decimals. Arts. 181 and 183. 5. Reduce .0625 lb. Troy to the frac. of an oz. Ans. .75 Ans. .8 Ans. .875 NOTE. When com. REVIEW.-185. What is Case 1? Rule for Case 1? fractions can not be exactly expressed in decimals, what is to be done? 186. What is Case 2? Rule for Case 2? NOTE. How find the value nearly of a decimal? 187. How reduce a decimal from a higher to a lower denomination? From a lower to a higher ? 8. Reduce .0004375 mi. to the frac. of a rd. Ans. .14 9. .25 pt. to the fraction of a gal. .6 pt. to the fraction of a bu. .3min. to the fraction of a da. 10. 11. Ans. .03125 Ans. .009375 Ans. .0002083+ Ans. .0021875 ART. 188. To find the value of a decimal in integers of a lower denomination. 1. Find the value of .3125 of a bu. SOLUTION. First multiply by 4, as in reducing bushels to peck 3. Art 81. This gives 1 peck and .25 of a peck; then find the value of .25 pk., by multiplying it by 8, the number of quarts in a peck. This gives 2 quarts; hence, .3125 of a bushel equals 1 pk. 2 qt. Ans. *2. Find the value of .875 of a yd. OPERATION. bu. .3125 4 pk. 1.2500 8 qt. 2.00 Ans. 3 qr. 2na. Rule for Case IV.-Multiply the given decimal by that number which will reduce it to the next lower denomination (Art. 81), and point the product, as in Multiplication (Art. 181). Reduce this decimal in like manner, and so on; the several integers on the left will be the required answer. FIND THE VALUE IN INTEGERS, 3.Of.7 4. b. of a lb. Troy. .8125 of a bu. .3375 of an A.. Ans. 8oz. 8pwt, Ans. 3 pk. 2qt. Ans. 1R. 14P. 6. .04318 of a mi. Ans. 13rd. 4yd. 1 ft. 5.8848 in. ART. 189. To reduce a quantity composed of one or more denominations, to the decimal of another quantity of one or more denominations. OPERATION 1. Reduce 2ft. 3 in. to the decimal of a yard. SOLUTION.-By Art. 163, the result expressed as a common fraction, is. This reduced to a decimal, becomes .75, the required answer. 2ft. 3 in. =27 in. lyd. =36 in. 27.75 Ans. *2. Reduce 2 pk. 4 qt. to the dec. of a bu. Ans. .625 Rule for Case V.—Reduce the first quantity and that of which it is to be made a part, both to the same denomination; the less will be the numerator, and the greater the denominator of a common fraction, which reduce to a decimal. 3. Red. 13 hr. 30 min. to the dec. of a da. Ans. .5625 4. 9 dr. to the dec. of a lb. Av. Ans. .03515625 5. .028 of a P. to the dec. of an A. Ans. .000175 6. 7 min. to the dec. of a da. Ans. .004881i+ 7. 4gal. 1qt. 1.28 pt. to the dec. of a hhd. Ans. .07 8. What part is 3pk. 7qt. 1pt. of 2bu. 2 pk. 4qt., expressed decimally? Ans. ,375 9. What part is 99 pages, of a book of 512 pages, expressed decimally. Ans. .193359375 10. What decimal will express the part that 55 A. 2R. 17 P. is of 229 A. 2 R. 16 P.? Ans. .2421875 ART. 190. PROMISCUOUS EXAMPLES. 1. What cost 9 yards of muslin, at $0.4 per yd., and 12 yards at $0.1875 per yd.? Ans. $5.85 2. What cost 2.3 yards of ribbon, at $0.45 per yd., and 1.5 yards at $0.375 per yd.? Ans. $1.5975 3. At $2.6875 per yd., what cost 16 yd. of cloth What 16 yd.? Ans. to last, $43.671875 4. At $0.75 per bushel, how much wheat can be bought for $35.25? Ans. 47 bu. REVIEW-188. What is Case 4? What the Rule for Case 4 189, What is Case 5? What the Rule for Case 5? |
