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  2. Guard digit - Wikipedia

    en.wikipedia.org/wiki/Guard_digit

    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} .

  3. Numeric precision in Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Numeric_precision_in...

    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 ...

  4. Round-off error - Wikipedia

    en.wikipedia.org/wiki/Round-off_error

    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 ...

  5. Rounding - Wikipedia

    en.wikipedia.org/wiki/Rounding

    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)

  6. Single-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Single-precision_floating...

    This gives from 6 to 9 significant decimal digits precision. If a decimal string with at most 6 significant digits is converted to the IEEE 754 single-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string. If an IEEE 754 single ...

  7. Decimal floating point - Wikipedia

    en.wikipedia.org/wiki/Decimal_floating_point

    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.

  8. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    An initial transient of max(a, b) digits after the decimal point. Some or all of the digits in the transient can be zeros. A subsequent repetend which is the same as that for the fraction ⁠ 1 / p k q ℓ ⋯ ⁠. For example ⁠ 1 / 28 ⁠ = 0.03 571428: a = 2, b = 0, and the other factors p k q ℓ ⋯ = 7; there are 2 initial non-repeating ...

  9. Positional notation - Wikipedia

    en.wikipedia.org/wiki/Positional_notation

    It was cursive by rounding off rational numbers smaller than 1 to 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64, with a 1/64 term thrown away (the system was called the Eye of Horus). A number of Australian Aboriginal languages employ binary or binary-like counting systems.