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Each decimal fraction has exactly two infinite decimal expansions, one containing only 0s after some place, which is obtained by the above definition of [x] n, and the other containing only 9s after some place, which is obtained by defining [x] n as the greatest number that is less than x, having exactly n digits after the decimal mark.
Most decimal fractions (or most fractions in general) cannot be represented exactly as a fraction with a denominator that is a power of two. For example, the simple decimal fraction 0.3 (3 ⁄ 10) might be represented as 5404319552844595 ⁄ 18014398509481984 (0.299999999999999988897769…). This inexactness causes many problems that are ...
A decimal fraction is a fraction whose denominator is an integer power of ten, commonly expressed using decimal notation, in which the denominator is not given explicitly but is implied by the number of digits to the right of a decimal separator.
A value is represented as a decimal fraction times a multiple power of 10. The factor is intended to make reading comprehension easier than a lengthy series of zeros. For example, 1.0 × 10 9 expresses one billion—1 followed by nine zeros. The reciprocal, one billionth, is 1.0 × 10 −9.
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
Muslim mathematicians were the first to utilize decimals instead of fractions on a large scale. Al-Kashi's book, Key to Arithmetic, was written at the beginning of the 15th century and was the stimulus for the systematic application of decimals to whole numbers and fractions thereof. [16] [17] But nobody established their daily use before ...
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A hundredth is written as a decimal fraction as 0.01, and as a vulgar fraction as 1/100. [2] “Hundredth” is also the ordinal number that follows “ninety-ninth” and precedes “hundred and first.” It is written as 100th.