8. Divide 27.101 by 1728. Anf. 015683+ Anf. 0387 9. Divide 02718 by 485-687.-Anf. ooco5596+. 10. Divide 000718 by 01856. CONTRACTED DIVISION, of DECIMALS. Operations in divifion of decimals may be much fhortened, and the quotient limited to any given number of decimal places, by observing the following RU L E. Find the value of the first figure in the quotient, which you may do by obferving that it will be of the fame value with that figure of the dividend which stands over the units place of the firft product in working the divifion. This will lead you to know how many figures in the dividend will be wanted to complete the answer. Make a mark over that decimal figure in the divisor which will be equal in divifion to the figures wanted in the dividend, and find how many times the divifor is contained in the dividend, rejecting thofe figures in the divifor which stand on the right hand of the mark you made. Let each remainder be a new dividend, and divide as before, only dropping a figure in the divifor at every operation, and carrying for all the figures you drop, when you multiply them, as directed in the rule for contracted multiplication of decimals. If the dividend or divifor has too few figures, add ciphers as you: fee neceffary. 1. Divide 72117562 by 2.257432, and let there be only three places of decimals in the quotient. Common Way. 2. Divide 61.41872 by 11.8718275, and let there be 4 places of decimals retained in the quotient. Anf. 5.1735. 3. Divide 217102 by 8-68759, and referve 3 places of decimals in the quotient. Anf. 2.499. 4. Divide 417.281 by 12·91641, and let the quotient contain 2 places of decimals. Anf 32.31. 5 Divide 165.9923 by 52.7438, and reserve 2 places of decimals in the quotient. Anf. 3.14. REDUCTION of DECIMALS. CA.SE I. To reduce a vulgar fraction to a decimal of the fame value. R U L E. Annex ciphers to the numerator and divide it by the denominator; continuing the operation as far as you fee neceffary, and the quotient will be the decimal required. EXAM PL E S. 1. Reduce to its equivalent decimal. 16)5·0000(*3125 Anf. 48 4. Reduce to equivalent decimals. 4285714, and 299465+. to its equivalent decimal. Anf. 22222. Τ of af of 7, and of of of 65 to equivalent decimals. Anf. 0243055, and ·027636+. 5. Exprefs of, and of of 17 decimally. Anf. 7619+, and 14875. 6. Let 4, 1, 3, 4, and be reduced to decimals. Anf. 25,—*5,— 333,—75,-8333, and •6666. CASE II. To reduce a decimal to its equivalent vulgar fraction. R U L E. If the decimal be a finite one; make it the numerator, and I, with as many ciphers as the decimal contains figures, the denominator. If the decimal be a repetend or a circulate; make the repeating figure or figures the numerator, and the denominator will be as many nines as there are repeating figures in the decimal. If there be a finite part before the repetend or circulate; fubtract the finite part from the whole mixed decimal, and the remainder will be the numerator, and the denominator will be 9 for each circulating figure with a cipher on the right hand for each finite decimal. EXAMPLES. 1. Reduce 375,-4444-345345,-and 37242424 to equivalent vulgar fractions. *375—1335 },—4444-3453453}}=}}}• *3724 3687 -=37242424. 9900 4. Required the vulgar fraction equivalent to 3333. Anf. + 5. Find the equivalent vulgar fraction to 185185185. Anf. 85 6. Let 14333 be reduced to an equivalent vulgar fraction. Anf. 43 7. Reduce 31275275 to its equivalent vulgar fraction. CASE III. Anf. 78 11 24975 To reduce money, weights, measures, &c. to equivalent decimals. If the quantity given be of but one denomination; divide it by as many as make one of the denomination fought, and the quotient will be the decimal required. -But if the quantity given be of more than one denomination; reduce it to the lowest name mentioned for a dividend, and reduce the integer to the fame name for a divifor, and find the quotient as before, which will be the answer. Different denominations may also be reduced to decimals of a specified integer, by placing the given names one under another, regularly from the least to the greateft, for dividends, and dividing these by their respective integers. Then, the laft quotient will be the decimal required. |