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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 ...
In decimal numbers greater than 1 (such as 3.75), the fractional part of the number is expressed by the digits to the right of the decimal (with a value of 0.75 in this case). 3.75 can be written either as an improper fraction, 375/100, or as a mixed number, 3 + 75 / 100 .
Also, some fractions (such as 1 ⁄ 7, which is 0.14285714285714; to 14 significant figures) can be difficult to recognize in decimal form; as a result, many scientific calculators are able to work in vulgar fractions or mixed numbers.
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.
It is useful because the number can be copied and pasted into calculators (including a web browser's omnibox) and parsed by the computer as-is (i.e., without the user manually purging the extraneous characters). For example, Wikipedia content can display numbers this way, as in the following examples: 149 597 870 700 metres is 1 astronomical unit
The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10 −2 power term, also called characteristics, [11] [12] [13] where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic: 123.45 = 12345 × 10 −2.
Sometimes this remainder is added to the quotient as a fractional part, so 10 / 3 is equal to 3 + 1 / 3 or 3.33..., but in the context of integer division, where numbers have no fractional part, the remainder is kept separately (or exceptionally, discarded or rounded). [5] When the remainder is kept as a fraction, it leads to a rational ...
The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form a/10 n, where a is an integer, and n is a non-negative integer. Decimal fractions also result from the addition of an integer and a fractional part; the resulting sum sometimes is called a fractional number.
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