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For example, if we want to round 1.2459 to 3 significant figures, then this step results in 1.25. If the n + 1 digit is 5 not followed by other digits or followed by only zeros, then rounding requires a tie-breaking rule. For example, to round 1.25 to 2 significant figures: Round half away from zero rounds up to 1.3.
In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9. With binary arithmetic, this rounding is also called "round to odd" (not to be confused with "round half to odd"). For example, when rounding to 1/4 (0.01 in binary), x = 2.0 ⇒ result is 2 (10.00 in binary)
A round number is an integer that ends with one or more "0"s (zero-digit) in a given base. [1] So, 590 is rounder than 592, but 590 is less round than 600. In both technical and informal language, a round number is often interpreted to stand for a value or values near to the nominal value expressed.
In mathematics and apportionment theory, a signpost sequence is a sequence of real numbers, called signposts, used in defining generalized rounding rules.A signpost sequence defines a set of signposts that mark the boundaries between neighboring whole numbers: a real number less than the signpost is rounded down, while numbers greater than the signpost are rounded up.
It is used to round the 33-bit approximation to the nearest 24-bit number (there are specific rules for halfway values, which is not the case here). This bit, which is 1 in this example, is added to the integer formed by the leftmost 24 bits, yielding: 11001001 00001111 1101101 1 _ . {\displaystyle 11001001\ 00001111\ 1101101{\underline {1}}.}
The text presently sayssaid that the round-half-to-even "rule will introduce a towards-zero bias when y − 0.5 is even". I assumes this means that with a set such as 2.5, 2.5, 4.5, 10.5, the result of rounding will be 2, 2, 4, 10, which has a towards-zero bias.