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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.
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]
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 ...
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.
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
A decimal separator is a symbol that separates the integer part from the ... Positional decimal fractions appear for the first time in a book by the Arab ...
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 ...
Such a decimal representation specifies the real number as the least upper bound of the decimal fractions that are obtained by truncating the sequence: given a positive integer n, the truncation of the sequence at the place n is the finite partial sum