1. TO WRITE A FRACTION WITH TEN, OR ANY POWER OF TEN POR ITS DENOMINATOR, AS A DECIMAL FRACTION. Rule. Mark off with a point as many figures as there are ciphers in the denominator, beginning from the right liand. If there be not enough figures in the numerator, write ciphers before to make up the number required. If there be too many, those that remain are the whole number which the fraction contains. EXAMPLES. 171 1345 27643 10101 Write as decimals. 10 100 1000 10000000 II. TO CONVERT A DECIMAL INTO A VULGAR FRACTION, OR THE SUM OF SEVERAL FRACTIONS. Rule. Form a fraction having for its numerator all the figures integral and decimal in the given decimal, and for its denominator 1, followed by as many ciphers as there are decimal figures; and reduce to its lowest terms. Or, form a series of fractions having the several decimal figures as numerators, and for denominator 1, followed by a number of ciphers equal to the distance of the figure from the point: the sum of these is the equivalent expression. EXAMPLES. 1. Convert 3.14159 into a vulgar fraction, and the sum of a series of fractions. 314159 100000 9 + + 111. Rule. Write the decimals under each other, so that the decimal points may be all in one column. Add the different columns together, as in common addition, and place the decimal point under the others. EXAMPLE. 3.14159 314.159 314159 + TO ADD DECIMALS. 314507.71649 Ans. IV. TO SUBTRACT DECIMALS. Rule. Write the smaller number under the greater, keeping the decimal points immediately under each other. Subtract each figure of the lower line from that above it, as in common Subtraction, supplying a cipher, whenever a figure occurs in one line, and not in the other. EXAMPLES. ). Subtract 3.87069 from 7.40168. 7.40168 3.53099 Ans. 2. Subtract 63.24108 from 147.84. 147.84 84.59892 Ans, D 2 3. Subtract .2709 from .4086382. .4086382 .1377382 Ans. V. TO MULTIPLY DECIMALS. Rule--1. To multiply by 10, 100, 1000, &c. remove the decimal point as many places to the right as there are ciphers in the multiplier, supplying ciphers on the right to make up any deficiency. 2. To multiply two decimal fractions, multiply as in whole numbers, and mark off in the product as many figures for decimals as there are decimals in the multiplier and multiplicand together. If there are not suficient figures in the product, supply ciphers on the left. EXAMPLES. 57.29577 X 10 = 572.9577 57.29577 X 1000000 = 57295770. 2. Multiply 21.0735 by .04683. 21.0735 .04683 632205 1685880 1264380 842940 .986869005 Ans. 3. Multiply .008207 by 7.056. .008207 7.056 49242 41035 574490 .057908592 Ans. VI. ABBREVIATED METHOD OF MULTIPLICATION OF DECIMALS, WHEN ONLY A CERTAIN NUMBER OF DECIMAL PLACES ARE REQUIRED IN THE PRODUCT. Rule-1. Reverse the multiplier, and place it under the multiplicand, so that what was the units' figure be under the last place of decimals to be retained, placing ciphers, if necessary, so that every figure in the multiplier may have a figure above it. 2. Multiply as usual, beginning each figure of the multiplier with that which is in the place to its right in the multiplicand; do not set down the figure of this product, but carry its nearest ten to the next, and proceed. 3. Place the first figures of all the products under one another ; add as usual, and mark off the required number of decimal places. EXAMPLE. Multiply .03281674 by 234.781 reserving six places of decimals. .03281674 187432 6563348 33 7.704746 Ans. VII. DIVISION OF DECIMALS. Rule-1. 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, supplying, if necessary, ciphers on the left. 2. To divide one decimal by another. Make the number of decimal places in the dividend at least equal to that of those in the divisor, by annexing ciphers on the right, if necessary, preceded by a point, if the dividend be a whole number. Divide as in whole numbers; and when all the figures of the dividend have been used, annex a cipher to each succeeding remainder, as far as the division may be carried. Mark off in the quotient as many figures for decimals as the number of decimal places in the dividend (including the ciphers annexed to the remainders) exceeds that of those in the divisor. EXAMPLES. 71634.3069 10 =7169.43069 45 =9X 5 2. Divide .0764183 by 45. .0764183 .008490922. |