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The otherwise binary Wang VS machine supported a 64-bit decimal floating-point format in 1977. [2] The Motorola 68881 supported a format with 17 digits of mantissa and 3 of exponent in 1984, with the floating-point support library for the Motorola 68040 processor providing a compatible 96-bit decimal floating-point storage format in 1990. [2]
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping.
For example, the smallest positive number that can be represented in binary64 is 2 −1074; contributions to the −1074 figure include the emin value −1022 and all but one of the 53 significand bits (2 −1022 − (53 − 1) = 2 −1074). Decimal digits is the precision of the format expressed in terms of an equivalent number of decimal digits.
This gives from 33 to 36 significant decimal digits precision. If a decimal string with at most 33 significant digits is converted to the IEEE 754 quadruple-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.
Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating. Finite decimal representations can also be seen as a special case of infinite repeating decimal representations. For example, 36 ⁄ 25 = 1.44 = 1.4400000...; the endlessly repeated sequence is the one-digit sequence "0".
By {{Convert}} default, the conversion result will be rounded either to precision comparable to that of the input value (the number of digits after the decimal point—or the negative of the number of non-significant zeroes before the point—is increased by one if the conversion is a multiplication by a number between 0.02 and 0.2, remains the ...
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 basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2] [3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that ...