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3.125 RPSP to 1/4 ⇒ result is 3.25; 3.25 RPSP to 1/2 ⇒ result is 3.5; 3.5 round-half-to-even to 1 ⇒ result is 4 (wrong) If the erroneous middle step is removed, the final rounding to integer rounds 3.25 to the correct value of 3. RPSP is implemented in hardware in IBM zSeries and pSeries.
For example, to round 1.25 to 2 significant figures: Round half away from zero rounds up to 1.3. This is the default rounding method implied in many disciplines [citation needed] if the required rounding method is not specified. Round half to even, which rounds to the nearest even number. With this method, 1.25 is rounded down to 1.2.
In IEEE 754 parlance, there are 10 bits of significand, but there are 11 bits of significand precision (log 10 (2 11) ≈ 3.311 decimal digits, or 4 digits ± slightly less than 5 units in the last place).
Thus the fraction 3 / 4 can be used to represent the ratio 3:4 (the ratio of the part to the whole), and the division 3 ÷ 4 (three divided by four). We can also write negative fractions, which represent the opposite of a positive fraction. For example, if 1 / 2 represents a half-dollar profit, then − 1 / 2 represents ...
A round number is mathematically defined as an integer which is the product of a considerable number of comparatively small factors [12] [13] as compared to its neighboring numbers, such as 24 = 2 × 2 × 2 × 3 (4 factors, as opposed to 3 factors for 27; 2 factors for 21, 22, 25, and 26; and 1 factor for 23).
Prices can also be quoted with a "plus", meaning one sixty-fourth (1/64) of one percent or half a tick. [2] That means that a price is quoted as, for instance, 99-30+, meaning 99 and 61/64 percent (or 30.5/32 percent) of the face value.
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
Here the 'IEEE 754 double value' resulting of the 15 bit figure is 3.330560653658221E-15, which is rounded by Excel for the 'user interface' to 15 digits 3.33056065365822E-15, and then displayed with 30 decimals digits gets one 'fake zero' added, thus the 'binary' and 'decimal' values in the sample are identical only in display, the values ...