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A decimal data type could be implemented as either a floating-point number or as a fixed-point number. In the fixed-point case, the denominator would be set to a fixed power of ten. In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied.
The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.
This gives from 6 to 9 significant decimal digits precision. If a decimal string with at most 6 significant digits is converted to the IEEE 754 single-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string. If an IEEE 754 single ...
^ The "classic" format is plain text, and an XML format is also supported. ^ Theoretically possible due to abstraction, but no implementation is included. ^ The primary format is binary, but text and JSON formats are available. [8] [9]
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
Generally, var, var, or var is how variable names or other non-literal values to be interpreted by the reader are represented. The rest is literal code. Guillemets (« and ») enclose optional sections.
The last 9 digit is the eighteenth fractional digit and thus the twentieth significant digit of the string. Bounds on conversion between decimal and binary for the 80-bit format can be given as follows: If a decimal string with at most 18 significant digits is correctly rounded to an 80-bit IEEE 754 binary floating-point value (as on input ...
To approximate the greater range and precision of real numbers, we have to abandon signed integers and fixed-point numbers and go to a "floating-point" format. In the decimal system, we are familiar with floating-point numbers of the form (scientific notation): 1.1030402 × 10 5 = 1.1030402 × 100000 = 110304.02. or, more compactly: 1.1030402E5