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A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [ 9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
A repeating decimal is an infinite decimal that, after some place, repeats indefinitely the same sequence of digits (e.g., 5.123144144144144... = 5.123 144). [4] An infinite decimal represents a rational number , the quotient of two integers, if and only if it is a repeating decimal or has a finite number of non-zero digits.
One half is a rational number that lies midway between nil and unity (which are the elementary additive and multiplicative identities) as the quotient of the first two non-zero integers, . It has two different decimal representations in base ten, the familiar and the recurring , with a similar pair of expansions in any even base; while in odd ...
The decimal representation represents the infinite sum : Every nonnegative real number has at least one such representation; it has two such representations (with if ) if and only if one has a trailing infinite sequence of 0, and the other has a trailing infinite sequence of 9. For having a one-to-one correspondence between nonnegative real ...
Any such symbol can be called a decimal mark, decimal marker, or decimal sign. Symbol-specific names are also used; decimal point and decimal comma refer to a dot (either baseline or middle ) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, [ 1 ] [ 2 ] [ 3 ] with the aforementioned ...
Decimal odds are favoured by betting exchanges because they are the easiest to work with for trading, as they reflect the inverse of the probability of an outcome. [13] For example, a quoted odds of 5.00 equals to a probability of 1 / 5.00, that is 0.20 or 20%. Decimal odds are also known as European odds, digital odds or continental odds. [9]
For example, in duodecimal, 1 / 2 = 0.6, 1 / 3 = 0.4, 1 / 4 = 0.3 and 1 / 6 = 0.2 all terminate; 1 / 5 = 0. 2497 repeats with period length 4, in contrast with the equivalent decimal expansion of 0.2; 1 / 7 = 0. 186A35 has period 6 in duodecimal, just as it does in decimal.
The base determines the fractions that can be represented; for instance, 1/5 cannot be represented exactly as a floating-point number using a binary base, but 1/5 can be represented exactly using a decimal base (0.2, or 2 × 10 −1).