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  2. 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 ...

  3. Kahan summation algorithm - Wikipedia

    en.wikipedia.org/wiki/Kahan_summation_algorithm

    = 2.80000 - 2.75987 As expected, the low-order parts can be retained in c with no or minor round-off effects. = 0.0401300 In this iteration, t was a bit too high, the excess will be subtracted off in next iteration. sum = 10005.9 Exact result is 10005.85987, sum is correct, rounded to 6 digits.

  4. Rounding - Wikipedia

    en.wikipedia.org/wiki/Rounding

    Rounding or rounding off means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ 23.4476 with $ 23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414. Rounding is often done to obtain a value that is easier to report and communicate than the ...

  5. Guard digit - Wikipedia

    en.wikipedia.org/wiki/Guard_digit

    As an example, consider the subtraction . Here, the product notation indicates a binary floating point representation with the exponent of the representation given as a power of two and with the significand given with three bits after the binary point.

  6. Numeric precision in Microsoft Excel - Wikipedia

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

    Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...

  7. Rome's iconic Trevi Fountain reopens after renovation work in ...

    www.aol.com/romes-iconic-trevi-fountain-reopens...

    Rome’s iconic Trevi Fountain reopened Sunday after three months of renovations, just in time for the inauguration of the 2025 Jubilee Holy Year that is expected to draw millions of visitors. To ...

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