rounding error

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rounding error

A student checks a calculator and sees a small rounding error in the result.

Definition
  1. Noun:
    • A computational inaccuracy: A "rounding error" is a small discrepancy or inaccuracy that arises when a numerical value is approximated to a specific number of digits or decimal places for convenience, rather than using its exact value. It is a type of quantitative miscalculation.
Usage
  • A "rounding error" is a technical term primarily used in mathematics, statistics, finance, and computer science to describe the inevitable, usually minor, loss of precision from the rounding process.
  • It is often discussed in the context of ensuring the accuracy of calculations, reports, or financial statements.
Examples
  • Noun:
    • The final sum was off by a few cents due to a rounding error.
    • In scientific computing, managing rounding error is crucial for reliable results.
    • The accountant explained that the discrepancy was just a rounding error.
Advanced Usage
  • Cumulative rounding error: When many rounded values are used in a sequence of calculations, the small individual errors can accumulate, leading to a significant total error.
    • The simulation's inaccuracy was caused by a cumulative rounding error over thousands of iterations.
Variants and Related Words
  • Round (verb): To express a number to a specified degree of accuracy (e.g., to the nearest whole number, tenth, or hundredth).
    • Round the result to two decimal places.
  • Truncation error (noun): A related but distinct type of error that results from cutting off digits without rounding (e.g., always rounding down).
Synonyms
  • Approximation error: A broader term for error resulting from any approximation method.
  • Numerical error: A general term for inaccuracies in numerical calculations.
Related Phrases
  • To be within rounding error: An expression indicating that a difference is so small it is insignificant and can be attributed to rounding.
    • The two estimates are essentially the same; the difference is within rounding error.
rounding error

A student checks a calculator and sees a small rounding error in the result.

Noun
  1. (mathematics) a miscalculation that results from rounding off numbers to a convenient number of decimals
    • the error in the calculation was attributable to rounding
    • taxes are rounded off to the nearest dollar but the rounding error is surprisingly small

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