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Numbers are represented in binary as IEEE 754 floating point doubles. Although this format provides an accuracy of nearly 16 significant digits, it cannot always exactly represent real numbers, including fractions. This becomes an issue when comparing or formatting numbers. For example:
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 nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common.
If an IEEE 754 double-precision number is converted to a decimal string with at least 17 significant digits, and then converted back to double-precision representation, the final result must match the original number. [1] The format is written with the significand having an implicit integer bit of value 1 (except for special data, see the ...
To represent the number 1,230,400 in normalized scientific notation, the decimal separator would be moved 6 digits to the left and × 10 6 appended, resulting in 1.2304 × 10 6. The number −0.004 0321 would have its decimal separator shifted 3 digits to the right instead of the left and yield −4.0321 × 10 −3 as a result.
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 sub-template takes a number and reformats it to only 3 digits and a dot (if needed), provided it's in the 0–999.9999..... range. It's used internally by {{Format price}} for producing pleasant looking numbers, and isn't meant to be called directly. Its behavior outside the specified range isn't planned for and will result in an undefined ...
In general, if b is the base, one writes a number in the numeral system of base b by expressing it in the form a n b n + a n − 1 b n − 1 + a n − 2 b n − 2 + ... + a 0 b 0 and writing the enumerated digits a n a n − 1 a n − 2... a 0 in descending order. The digits are natural numbers between 0 and b − 1, inclusive.