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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.
Thus, it is often useful to convert repeating decimals into fractions. A conventional way to indicate a repeating decimal is to place a bar (known as a vinculum) over the digits that repeat, for example 0. 789 = 0.789789789... For repeating patterns that begin immediately after the decimal point, the result of the conversion is the fraction ...
The final conversion is from binary to decimal fractions. The only difficulty arises with repeating fractions, but otherwise the method is to shift the fraction to an integer, convert it as above, and then divide by the appropriate power of two in the decimal base.
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 ...
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
Conversion of the fractional part: Consider 0.375, the fractional part of 12.375. To convert it into a binary fraction, multiply the fraction by 2, take the integer part and repeat with the new fraction by 2 until a fraction of zero is found or until the precision limit is reached which is 23 fraction digits for IEEE 754 binary32 format.
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45 ). Different countries officially designate different symbols for use as the separator.
Q (number format) 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.