Rounding Numbers: Rules and Examples

Rounding replaces a number with a nearby, simpler one to a chosen level of precision. The everyday rule is "round half up": look at the first digit you're dropping, round up if it's 5 or more, and round down if it's 4 or less. So 2.5 rounds to 3 and 2.4 rounds to 2. You can round to decimal places or significant figures in a click with our free rounding calculator.

Round half up: the everyday rule

Find the place you're rounding to, then check the digit right after it. If that digit is 5, 6, 7, 8, or 9, round the kept digit up by one; if it's 0, 1, 2, 3, or 4, leave it as is. Rounding 2.7 to the nearest whole number gives 3, and 2.3 gives 2. This is the convention most classrooms use unless told otherwise.

Rounding to decimal places

Rounding to a number of decimal places means keeping that many digits after the decimal point. Rounding 3.14159 to two decimal places gives 3.14, because the next digit (1) is less than 5. Rounding the same number to three decimal places gives 3.142, since the next digit (5) rounds up.

Rounding to significant figures

Rounding to significant figures counts meaningful digits starting from the first non-zero digit rather than from the decimal point. Rounding 3.14159 to three significant figures gives 3.14, while a small number like 0.004678 rounded to two significant figures gives 0.0047. If sig figs are new to you, our significant figures calculator breaks down the counting.

COSMIQ — Demo — Math manipulatives

Round half to even (banker's rounding)

There's a second convention worth knowing. Round half to even, sometimes called banker's rounding, sends an exact half to the nearest even digit to reduce bias over many calculations: 2.5 rounds to 2, but 3.5 rounds to 4. Spreadsheets and some programming languages use this, so don't be surprised if a computer disagrees with the half-up rule by one.

Rounding to the nearest 10, 100, or 1000

The same logic scales up to whole-number place values. Rounding 1480 to the nearest hundred gives 1500 (the tens digit, 8, rounds up), while rounding 1480 to the nearest thousand gives 1000 (the hundreds digit, 4, rounds down). Always look only at the single digit just to the right of your target place.

COSMIQ — Home — COSMIQ landing page

Round it right, every time

When you want a fast, correct result to any precision, use the rounding calculator, and for compactly writing very large or small rounded values, try the scientific notation converter. To talk through when to round and how, COSMIQ's free voice tutor is free for every learner.