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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.
The Q notation is a way to specify the parameters of a binary fixed point number format. For example, in Q notation, the number format denoted by Q8.8 means that the fixed point numbers in this format have 8 bits for the integer part and 8 bits for the fraction part. A number of other notations have been used for the same purpose.
Decimal degrees (DD) is a notation for expressing latitude and longitude geographic coordinates as decimal fractions of a degree. DD are used in many geographic information systems (GIS), web mapping applications such as OpenStreetMap, and GPS devices. Decimal degrees are an alternative to using degrees-minutes-seconds notation. As with ...
Where numerator and denominator can each be expressed in one word, a fraction is usually spelled out (e.g. a two-thirds majority; moved one-quarter mile); use figures if a fraction appears with a unit symbol (e.g. 1 ⁄ 4 mi (markup: {{frac|1|4}} mi), not a quarter of a mi or one-quarter mi).
A decrease of 60% means the final amount is 40% of the original (100% – 60% = 40%). A decrease of 100% means the final amount is zero (100% – 100% = 0%). In general, a change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount (equivalently, (1 + 0.01 x ) times the original amount).
Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
This format uses a binary significand from 0 to 10 p −1. For example, the Decimal32 significand can be up to 10 7 −1 = 9 999 999 = 98967F 16 = 1001 1000100101 1001111111 2 . While the encoding can represent larger significands, they are illegal and the standard requires implementations to treat them as 0, if encountered on input.