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  2. 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 ...

  3. 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 ...

  4. 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)

  5. Catastrophic cancellation - Wikipedia

    en.wikipedia.org/wiki/Catastrophic_cancellation

    Given numbers and , the naive attempt to compute the mathematical function by the floating-point arithmetic ⁡ (⁡ ⁡ ()) is subject to catastrophic cancellation when and are close in magnitude, because the subtraction can expose the rounding errors in the squaring.

  6. Significant figures - Wikipedia

    en.wikipedia.org/wiki/Significant_figures

    If this method applies to 1.35, then it is rounded up to 1.4. This is the method preferred by many scientific disciplines, because, for example, it avoids skewing the average value of a long list of values upwards. For an integer in rounding, replace the digits after the n digit with zeros. For example, if 1254 is rounded to 2 significant ...

  7. Round number - Wikipedia

    en.wikipedia.org/wiki/Round_number

    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.

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  9. Decimal data type - Wikipedia

    en.wikipedia.org/wiki/Decimal_data_type

    Some programming languages (or compilers for them) provide a built-in (primitive) or library decimal data type to represent non-repeating decimal fractions like 0.3 and −1.17 without rounding, and to do arithmetic on them. Examples are the decimal.Decimal or num7.Num type of Python, and analogous types provided by other languages.