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The choice between fraction and decimal notation is often a matter of taste and context. Fractions are used most often when the denominator is relatively small. By mental calculation, it is easier to multiply 16 by 3 ⁄ 16 than to do the same calculation using the fraction
Every decimal representation of a rational number can be converted to a fraction by converting it into a sum of the integer, non-repeating, and repeating parts and then converting that sum to a single fraction with a common denominator.
Every terminating decimal representation can be written as a decimal fraction, a fraction whose denominator is a power of 10 (e.g. 1.585 = 1585 / 1000 ); it may also be written as a ratio of the form k / 2 n ·5 m (e.g. 1.585 = 317 / 2 3 ·5 2 ).
Decimal fractions (sometimes called decimal numbers, especially in contexts involving explicit fractions) are the rational numbers that may be expressed as a fraction whose denominator is a power of ten. [8]
First, every nonzero number with a finite decimal notation (equivalently, endless trailing 0s) has a counterpart with trailing 9s. For example, 0.24999... equals 0.25, exactly as in the special case considered. These numbers are exactly the decimal fractions, and they are dense. [41] [9] Second, a comparable theorem applies in each radix (base).
A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum ... which adds at least three decimal digits per ...
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 ...
Hence, even if decimal fractions were used previously by other men, it was STEVIN – and no other – who introduced them into the mathematical domain. That important extension of the idea of number – the creation of the decimal number – was undoubtedly a fruit of his genius, and its occurrence can be very exactly dated – 1585." [1]: 162