Rounding Calculator

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How Rounding Works

Rounding replaces a number with an approximation that is easier to work with, while keeping the value as close to the original as possible. The standard rounding rule: if the digit being dropped is 5 or greater, round up. If it is less than 5, round down (keep the preceding digit the same).

Rounding errors can accumulate in long chains of calculations. In financial and scientific work, it is generally best to carry extra precision through all intermediate steps and round only the final result. Rounding at each intermediate step introduces small errors that compound into larger ones.

Ceiling and Floor

The ceiling function always rounds up to the next whole number, regardless of the decimal value. The floor function always rounds down. These differ from standard rounding, which rounds to the nearest value. A price of $3.10 rounded to the nearest dollar is $3. The ceiling is $4. The floor is $3.

Significant Figures

Significant figures (sig figs) are a different concept from decimal places. Decimal places count digits after the decimal point. Significant figures count all meaningful digits in a number, starting from the first non-zero digit. The number 0.00456 has three significant figures but five decimal places. This calculator rounds to decimal places, which is appropriate for most everyday uses.