Search results
Results From The WOW.Com Content Network
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.
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.
A real number is computable if its digit sequence can be produced by some algorithm or Turing machine. The algorithm takes an integer as input and produces the -th digit of the real number's decimal expansion as output. (The decimal expansion of a only refers to the digits following the decimal point.)
These two representations are identical, unless x is a decimal fraction of the form . In this case, in the first decimal representation, all are zero for >, and, in the second representation, all 9. (see 0.999... for details).
The choice between fraction and decimal notation is often a matter of taste and context. Fractions are used most often when the denominator is relatively small. By mental calculation, it is easier to multiply 16 by 3 ⁄ 16 than to do the same calculation using the fraction
That is, fractions aren't difficult to compare if the numerator is 1 (e.g., 1 ⁄ 2 is larger than 1 ⁄ 3, which in turn is larger than 1 ⁄ 4). However, comparisons become more difficult when both numerators and denominators are mixed: 3 ⁄ 4 is larger than 5 ⁄ 7 , which in turn is larger than 2 ⁄ 3 , though this cannot be determined by ...
Six hexadecimal digits of precision is roughly equivalent to six decimal digits (i.e. (6 − 1) log 10 (16) ≈ 6.02). A conversion of single precision hexadecimal float to decimal string would require at least 9 significant digits (i.e. 6 log 10 (16) + 1 ≈ 8.22) in order to convert back to the same hexadecimal float value.