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Excel has the option to "Set precision as displayed". [c] With this option, depending upon circumstance, accuracy may turn out to be better or worse, but you will know exactly what Excel is doing. (Only the selected precision is retained, and one cannot recover extra digits by reversing this option.) Some similar examples can be found at this ...
When using approximation equations or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits), one of the goals of numerical analysis is to estimate computation errors. [5] Computation errors, also called numerical errors, include both truncation errors and roundoff errors.
False precision (also called overprecision, fake precision, misplaced precision, and spurious precision) occurs when numerical data are presented in a manner that implies better precision than is justified; since precision is a limit to accuracy (in the ISO definition of accuracy), this often leads to overconfidence in the accuracy, named precision bias.
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 ...
P formatting Excel style cell format specification; F record Use: Format If P record(s) are present, follows them. Possible fields: X column column (one based) Y row row (one based) C column column (one based) R row row (one based) F format Cell/row/column format The format of format is ch1 digits ch2 ch1 is D default C currency E exponent F ...
The 53-bit significand precision gives from 15 to 17 significant decimal digits precision (2 −53 ≈ 1.11 × 10 −16). If a decimal string with at most 15 significant digits is converted to the IEEE 754 double-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final ...
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
The digits in the base and exponent (10 3 or 10 −2) are considered exact numbers so for these digits, significant figures are irrelevant. Explicitly state the number of significant figures (the abbreviation s.f. is sometimes used): For example "20 000 to 2 s.f." or "20 000 (2 sf)".