Rounding

Rounding replaces a number with a nearby value that has fewer significant digits or a simpler form. The result depends on the chosen precision and rounding rule.

Round half to even: A rounding rule that sends exact halfway cases to the nearest even result. It reduces systematic upward bias when many values are rounded.
Round-off error: The difference between an exact value and its finite-precision representation or rounded approximation. It quantifies the discrepancy introduced by replacing a number with a nearby value.
Measurement uncertainty: The quantified doubt associated with a measured value, arising from instruments, methods, and other influences. Reported digits should reflect measurement uncertainty rather than imply unwarranted precision.
Floor function: The function that maps each real number to the greatest integer less than or equal to it. It always moves toward negative infinity, not to the nearest value.
Round half up: A rounding rule that sends exact halfway cases to the greater value in magnitude. It is the familiar school rule for deciding exact ties.
Floating-point arithmetic: Computer arithmetic that represents real numbers using a finite significand and a scaled exponent. Its finite representations require rounding during many computations.
Significant figures in measurement: A convention for expressing measurement precision through the number of reported significant digits. It guides how measured values are rounded for reporting.
Ceiling function: The function that maps each real number to the least integer greater than or equal to it. It always moves toward positive infinity rather than choosing the nearest integer.
Truncation: A number operation that discards digits beyond a specified position without adjusting the retained digits. Unlike rounding, it always removes the discarded part rather than choosing the nearest value.
Numerical stability: A property of an algorithm whose output changes only modestly under small computational perturbations. Stable algorithms limit how rounding errors affect computed answers.

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