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This variant of the round-to-nearest method is also called convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding, [6] or bankers' rounding. [ 7 ] This is the default rounding mode used in IEEE 754 operations for results in binary floating-point formats.
The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if the number 1300 is precise to the nearest unit (just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundreds due to rounding or uncertainty.
The IEEE standard uses round-to-nearest. Round-by-chop: The base-expansion of is truncated after the ()-th digit. This rounding rule is biased because it always moves the result toward zero. Round-to-nearest: () is set to the nearest floating-point number to . When there is a tie, the floating-point number whose last stored digit is even (also ...
In decimal notation, a number ending in the digit "5" is also considered more round than one ending in another non-zero digit (but less round than any which ends with "0"). [2] [3] For example, the number 25 tends to be seen as more round than 24. Thus someone might say, upon turning 45, that their age is more round than when they turn 44 or 46.
|-N (where -N is a negative number) replaces N digits before the decimal mark with zero (round output to nearest 10 N). |sigfig=N (where N is a positive number) to specify the number of significant digits (round output to N significant figures). |round=5 to round the output to the nearest multiple of 5. The round value can be 0.5, 5, 10, 25 or ...
To round a number to its nearest order of magnitude, one rounds its logarithm to the nearest integer. Thus 4 000 000, which has a logarithm (in base 10) of 6.602, has 7 as its nearest order of magnitude, because "nearest" implies rounding rather than truncation. For a number written in scientific notation, this logarithmic rounding scale ...
Round to nearest, ties to even – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value with an even least significant digit. Round to nearest, ties away from zero (or ties to away ) – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value above (for positive numbers ...
The hands value has at most one digit after the decimal mark, and has an optional fraction. A precision of 2 assumes |frac=2 (round to nearest 1 ⁄ 2 inch). A precision of 3 or more assumes |frac=4 (round to nearest 1 ⁄ 4 inch). If ever needed, |frac=8 can be used to round to the nearest 1 ⁄ 8 inch. {{convert|27.63|in|hand}} → 27.63 ...