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Round numbers to nearest integer, specific decimal places, or significant figures. Shows floor and ceiling values.
Rounding Rules:
Round half up: if digit >= 5, round up; else round down
To n decimal places: round(x * 10^n) / 10^n
To n significant figures: based on position of first non-zero digit
Floor: largest integer less than or equal to x
Ceiling: smallest integer greater than or equal to x
Rounding replaces a number with an approximation that has fewer significant digits. The standard rule is to round up when the dropped digit is 5 or more, and round down when it is less than 5.
Significant figures are the meaningful digits in a number. For example, 3.14 has 3 significant figures. Leading zeros (0.005) are not significant; trailing zeros after a decimal point are (3.500 has 4 significant figures).
Floor rounds down to the nearest integer: floor(3.7) = 3, floor(-3.7) = -4. Ceiling rounds up: ceil(3.2) = 4, ceil(-3.2) = -3.
Significant figures are used in scientific measurements to indicate the precision of a value. The result of a calculation should not have more significant figures than the least precise input.
Banker's rounding (round half to even) rounds 0.5 to the nearest even number: 2.5 rounds to 2, 3.5 rounds to 4. This reduces cumulative rounding error in large datasets.