DECIMAL FRACTION, a fraction whose denominator is a decimal or 1234 power of 10. Thus — is a decimal 100 fraction. It may be decomposed into the sum 1000 200 30 4 —— — — 100 100 100 100 3 4=10 + 2 + — 10 100By an obvious extension of the method of local values, where each digit has 10 times the value of the like digit which immediately succeeds it, the above deci mal fraction may clearly be written more concisely in the form 12.34, where the decimal point after the two merely serves to indicate which digit represents units. In this abbreviated form a deci mal fraction is termed a decimal. For the purpose of indicating the unit's place, other and less objectionable meth ods have been proposed. Sir Isaac Newton's method, however, of using a point, placed for distinction near the top of the figures, is the one most commonly employed. The operations of addition, subtraction, multiplication, anddivi sion may be applied to decimals in ex actly the same manner as to integers; hence their great utility. They present, nevertheless, this disadvantage, that comparatively few fractional quantities or remainders can be exactly expressed by them; in other words, the greater number of common fractions cannot be reduced, as it is called, to decimal frac tions, without leaving a remainder.
Common fractions, such as 1-2, 2-3, 1-4, 3-7, and 9-25, for instance, can be re duced to decimal fractions only by mul tiplying the numerator and denominator of each by such a number as will convert the denominator into 10, or 100, 1,000, etc. (The common process is merely an abridgement of this.) But that is pos sible only when the denominator divides 10, or 100, without remainder. Thus, of the above denominators, 2 is con tained in 10, 5 times; 4 in 100, 25 times; and 25 in 100, 4 times; therefore, 1 I X 5 5 1 1 X 25 .5; 2 2 x 5 10 4 4 x 25 25 9 9 X 4 36 = — = .25 ; — = = -- .36 100 25 25 X 4 100 But neither 3 nor 7 will divide 10, or any power of 10; and therefore these numbers cannot produce powers of 10 by multiplication. In such cases we can only approximate to the value of the fraction.