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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, the last digit, in binary form, is equal ...
Approximating a fraction by a fractional decimal number: 5 / 3 1.6667: 4 decimal places: Approximating a fractional decimal number by one with fewer digits 2.1784: 2.18 2 decimal places Approximating a decimal integer by an integer with more trailing zeros 23217: 23200: 3 significant figures Approximating a large decimal integer using ...
For numbers with a base-2 exponent part of 0, i.e. numbers with an absolute value higher than or equal to 1 but lower than 2, an ULP is exactly 2 −23 or about 10 −7 in single precision, and exactly 2 −53 or about 10 −16 in double precision. The mandated behavior of IEEE-compliant hardware is that the result be within one-half of a ULP.
For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with 8 decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on.
After padding the second number (i.e., ) with two s, the bit after is the guard digit, and the bit after is the round digit. The result after rounding is 2.37 {\displaystyle 2.37} as opposed to 2.36 {\displaystyle 2.36} , without the extra bits (guard and round bits), i.e., by considering only 0.02 + 2.34 = 2.36 {\displaystyle 0.02+2.34=2.36} .
In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks .
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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.