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TAE Marine. REVIEW : , 17 places as the number of decimal places in the dividend ex- ceeds those in the divisor. Before commencing the division, the number of decimal places in the dividend should be made at least equal to the number of decimal places in the divisor. When there is a remainder after using all the figures of the dividend annex decimal ciphers and continue the division. For all practical purposes, it is not necessary to carry the division further than to obtain four or five decimal figures in the quotient. Divide 14.625 by 3.25. 3.25 ) 14.625 (4.5 1300 . 1625 1625 In this example there are two decimal places in the di- visor and three in the dividend; hence, there is one decimal place in the quotient. Divide 9.6 by .06. .06 ) 9.60 ( 160 6 36 36 oO Here, by affixing a cipher to 9.6, it becomes 9.60, and has then two decimal places in it, which is the same number as in the divisor; therefore, the quotient is a whole number. If the quotient does not contain a sufficient number of deci- mal places, the deficiency must be supplied by prefixing ci- phers. When there is a remainder after using all the figures of the dividend, annex decimal ciphers and continue the division. Divide .00864 by .24. .24 ) .00864 ( .036 72 144 "TAA Explanation--The numbers are divided as if they were whole numbers. Since the dividend contains five decimal places, and the divisor two, the quotient contains 5 minus 2, - or 3 decimal places. Since there are only two figures in the quotient, a cipher is prefixed to make the required number of decimal places. Divide 3.1 by .0062. 0062 ) 3.100000 ( 500.00 3.10 "00000 Therefore, the answer is 500.00, Or 500. Rule.--Divide as in division of whole numbers and from the right of the quotient point off as many figures BS the decimal places in the dividend exceed those in the divisor. Here is another rule for pointing off: Subtract the number of decimal places in the divisor from those in the dividend and with the remainder left, if any, point off the quotient, ward the left. Starting with the last figure and moving to Note--In a great many examples it is necessary to add ciphers to the dividend, each cipher added counting as a deci- mal place. This is on the same principle and rule of con- verting a common fraction to a decimal fraction. It is neces- sary in a great many cases to add ciphers in order to have the quotient come even. ee Divide .75 by .25. If you have the same number 0 ecima places in the divisor as in the dividend there will be none in the quotient. You know from common sense that %4 goes into 34, 3 times. . Divide .75 by .s, 5) 75 G15 5 25 S 25 --_--_ One decimal place in the divisor and two in the dividend, and one from two is one, so there is one decimal place in the quotient. Divide 75 by .25 (remember 75 whole ones). The dividend must contain as many decimal places as there are decimal places in the divisor. If not, then add enough ciphers to supply the shortage, as follows: -25 ) 75.00 ( 300 75 Oo Oo There are the same number of decimal places, two, in the divisor as in the dividend in the above example; so two from two leaves nothing, therefore, there will be none in the quo- tient. To prove an example in division multiply the quotient and divisor, and if correct the product will equal the dividend; thus : ; .25 X 300 75.00 -- dividend Divide 81.6 by 3.6 = 22.66 2-3. 675 = .15 = 4500. 952 +. 4.76 = .2. 88.476 + 1.2 = 73.73.: 0026 + .003 = 8 2-3. : If 64 tons of iron costs $4,816, how many tons can be bought for $1,730.75? Ans. 23 tons. Note.--A decimal that will not divide an equal number of times, or has a remainder, is called a repeating decimal, that is, you could keep on dividing forever with the same result. Whenever you come to one of them just work it out to two or three decimal places, which is close enough for all practical purposes. For example, 1-3 to a decimal. 3) 3000 (.a3ar .333 is the decimal fraction for 1-3. Do you see that you could keep on dividing forever and have the same result? Note.--If the number of figures in the quotient be Jess than the ex- cess of the decimal places in the dividend over those in the divisor, the deficiency must be supplied by prefixing 'ciphers. : If there be a remainder after dividing the dividend, annex ciphers and continue the division: the ciphers annexed are decimals of the dividend. _--In common fractions the unit may be divided into halves, ac fourths, fifths, sixths, sevenths, eighths, ninths, tenths, elev- enths, and so on indefinitely. In decimals the division of the unit" starts with tenths--one-tenth, two-tenths, three, four, five, six, seven, eight, nine--tenths. The next lower denomination of divisions is 100ths. One one-hundredth (1-100) means one out of hundred, the unit is divided into 100 equal parts and the one is one of the 100 parts. The numerator can then be 1 to 99 of the 100 parts. Ten-tenths is a whole one; so is 100 100ths a whole one; 5-10 is Ys, so is 50-100. The next lower denomination of divisions is 1000 of which it takes 1000 parts to make a whole one. .5, .50, .500 are all the same thing, being equal to %. In the first decimal 10 is the denominator and 5 represents 5 of the 10 parts, and as 5 is one-half of 10, the fraction must be %; in the second decimal the denominator 'or unit is divided into 100 equal parts; .50 represents the numerator and shows how many times