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Some programming languages (or compilers for them) provide a built-in (primitive) or library decimal data type to represent non-repeating decimal fractions like 0.3 and −1.17 without rounding, and to do arithmetic on them. Examples are the decimal.Decimal or num7.Num type of Python, and analogous types provided by other languages.
A variable or value of that type is usually represented as a fraction m/n where m and n are two integer numbers, either with a fixed or arbitrary precision.Depending on the language, the denominator n may be constrained to be non-zero, and the two numbers may be kept in reduced form (without any common divisors except 1).
[nb 2] For instance rounding 9.46 to one decimal gives 9.5, and then 10 when rounding to integer using rounding half to even, but would give 9 when rounded to integer directly. Borman and Chatfield [ 15 ] discuss the implications of double rounding when comparing data rounded to one decimal place to specification limits expressed using integers.
In most ALGOL-like languages, such as Pascal, Modula-2, Ada and Delphi, conversion and casting are distinctly different concepts. In these languages, conversion refers to either implicitly or explicitly changing a value from one data type storage format to another, e.g. a 16-bit integer to a 32-bit integer. The storage needs may change as a ...
One with a binary integer significand field encodes the significand as a large binary integer between 0 and 10 p −1. This is expected to be more convenient for software implementations using a binary ALU. Another with a densely packed decimal significand field encodes decimal digits more directly. This makes conversion to and from binary ...
Like the binary16 and binary32 formats, decimal32 uses less space than the actually most common format binary64.. In contrast to the binaryxxx data formats the decimalxxx formats provide exact representation of decimal fractions, exact calculations with them and enable human common 'ties away from zero' rounding (in some range, to some precision, to some degree).
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The standard type hierarchy of Python 3. In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. [1]