How to Round Numbers: Round Half Up, Round Half to Even, and More

Decimal places versus significant figures

Rounding to decimal places counts from the decimal point, no matter how big the number is. Rounding 0.086 to two decimal places gives 0.09, and rounding 152.086 to two decimal places gives 152.09. Rounding to significant figures instead counts meaningful digits from the first non-zero digit, so 0.086 to one significant figure is 0.09, but 152 to one significant figure is 200.

The distinction matters because the two can disagree sharply for very large or very small numbers. A width of 0.004821 m rounded to two decimal places collapses to 0.00 — losing all the information — while rounded to two significant figures it is a useful 0.0048. Choose decimal places when a fixed precision is required (like cents in money), and significant figures when relative precision is what counts.

Round half up: the everyday method

Round half up is what most people learn in school. Look at the first digit being dropped: if it is 5, 6, 7, 8, or 9, add one to the kept digit; if it is 0, 1, 2, 3, or 4, leave the kept digit alone. Rounding 7.5 to a whole number gives 8, and 7.4 gives 7. It is simple and predictable, which is why it dominates everyday arithmetic.

There is a hidden flaw, though: round half up always pushes exact halves upward, so over many numbers it nudges the total slightly high. For a shopping receipt this bias is trivial. For millions of transactions or a large dataset, that consistent upward drift becomes real money or a skewed statistic — which is exactly where the next method earns its keep.

Round half to even (banker's rounding)

Round half to even, also called banker's rounding, treats exact halves specially: it rounds them to whichever neighbor is even. So 2.5 goes to 2, 3.5 goes to 4, 4.5 goes to 4, and 5.5 goes to 6. Any value that is not exactly a half follows the usual nearest rule — 2.51 still rounds to 3. Only the tie-breaking case changes.

Because ties go up half the time and down half the time, the rounding errors cancel out across a large batch, leaving the sum unbiased. This is why it is the default in the IEEE 754 floating-point standard your computer uses and in much financial and statistical work. If you round many values and then add them, round half to even keeps the total honest.

Frequently asked questions

What does round half up do with negative numbers?

It depends on the exact convention. Round half up on magnitude sends −2.5 to −3, while round half toward positive infinity sends it to −2. Agree on the direction before you start, since the two differ only on exact halves but can matter over many values.

Why does 2.5 round to 2 in my spreadsheet?

Your tool is using round half to even. Since 2 is the even neighbor of 2.5, the tie breaks downward. Many programming languages and financial systems default to this rule to avoid the upward bias of round half up.

How do I round to the nearest ten or hundred?

Look at the digit one place to the right of your target. To round 3847 to the nearest hundred, the tens digit is 4, so you round down to 3800. To the nearest ten, the ones digit is 7, so you round up to 3850.

Is truncating the same as rounding?

No. Truncating simply drops the extra digits without looking at them, so 3.19 truncated to one decimal is 3.1, not 3.2. Rounding considers the next digit and can go up, which usually makes it more accurate than truncation.