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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 ).
Any integer can be written as a fraction with the number one as denominator. For example, 17 can be written as 17 / 1 , where 1 is sometimes referred to as the invisible denominator. [17] Therefore, every fraction and every integer, except for zero, has a reciprocal. For example, the reciprocal of 17 is 1 / 17 .
Any binary fraction a/2 m, such as 1/16 or 17/32, can be exactly represented in fixed-point, with a power-of-two scaling factor 1/2 n with any n ≥ m. However, most decimal fractions like 0.1 or 0.123 are infinite repeating fractions in base 2. and hence cannot be represented that way. Similarly, any decimal fraction a/10 m, such as 1/100 or ...
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping.
In medieval Latin texts, sexagesimal numbers were written using Arabic numerals; the different levels of fractions were denoted minuta (i.e., fraction), minuta secunda, minuta tertia, etc. By the 17th century it became common to denote the integer part of sexagesimal numbers by a superscripted zero, and the various fractional parts by one or ...
For example, the decimal number 123456789 cannot be exactly represented if only eight decimal digits of precision are available (it would be rounded to one of the two straddling representable values, 12345678 × 10 1 or 12345679 × 10 1), the same applies to non-terminating digits (. 5 to be rounded to either .55555555 or .55555556).
The unit fractions are the rational numbers that can be written in the form , where can be any positive natural number. They are thus the multiplicative inverses of the positive integers. When something is divided into n {\displaystyle n} equal parts, each part is a 1 / n {\displaystyle 1/n} fraction of the whole.
However, this relaxed form of Egyptian fractions does not allow for any number to be represented using fewer fractions, as any expansion with repeated fractions can be converted to an Egyptian fraction of equal or smaller length by repeated application of the replacement + = + + (+) if k is odd, or simply by replacing 1 / k + 1 / k ...