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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 .
In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number 5 / 74 : 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.
If the given number is in decimal and the target base is duodecimal, the method is same. Using the digit conversion tables: (decimal) 10,000 + 2,000 + 300 + 40 + 5 + 0.6 = (duodecimal) 5,954 + 1,1A8 + 210 + 34 + 5 + 0; 7249. To sum these partial products and recompose the number, the addition must be done with duodecimal rather than decimal ...
Any such decimal fraction, i.e.: d n = 0 for n > N, may be converted to its equivalent infinite decimal expansion by replacing d N by d N − 1 and replacing all subsequent 0s by 9s (see 0.999...). In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion.
When converting to a larger base (such as from binary to decimal), the remainder represents as a single digit, using digits from . For example: converting 0b11111001 (binary) to 249 (decimal): For example: converting 0b11111001 (binary) to 249 (decimal):
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. For example, to convert. 8.123 {\textstyle \pm 8.123 {\overline {4567}}} to a fraction one notes the lemma:
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