Rounding to the nearest integer means replacing a decimal number with the closest whole number. If you have 3.7, the nearest integer is 4. If you have 3.2, the nearest integer is 3. The core idea is simple: which whole number is this decimal closest to on a number line?
What “Nearest Integer” Actually Means
An integer is any whole number, whether positive, negative, or zero. So 5, -12, and 0 are all integers. Numbers like 3.7, -1.6, and 0.25 are not integers because they have decimal parts.
When you round to the nearest integer, you’re finding the whole number that sits closest to your original number. Think of it on a number line: 3.7 sits between 3 and 4, but it’s closer to 4. So 3.7 rounds to 4. Meanwhile, 3.2 also sits between 3 and 4, but it’s closer to 3. So 3.2 rounds to 3.
The Basic Rule
You only need to look at the first digit after the decimal point (the tenths place) to decide which way to round:
- Tenths digit is 0, 1, 2, 3, or 4: Round down. The ones digit stays the same. Example: 6.3 rounds to 6.
- Tenths digit is 5, 6, 7, 8, or 9: Round up. The ones digit increases by 1. Example: 6.7 rounds to 7.
It doesn’t matter how many decimal places the original number has. Whether it’s 6.3 or 6.3149, you look at the tenths digit (3) and round accordingly. Both round to 6.
What Happens With .5
The tricky case is when a number falls exactly halfway between two integers, like 2.5. It’s equally close to 2 and 3, so there’s no single “nearest” integer. Different fields handle this differently.
The most common rule taught in schools is “round half up,” meaning 2.5 rounds to 3, 7.5 rounds to 8, and so on. This is also standard in most financial calculations.
In computing and statistics, a different method called “round half to even” (sometimes called banker’s rounding) is the default. Under this rule, 2.5 rounds to 2 (the nearest even number) while 3.5 rounds to 4 (also the nearest even number). This approach prevents a systematic upward bias when you’re rounding thousands of numbers, since roughly half the time the .5 goes up and half the time it goes down. It’s the default rounding mode in the IEEE 754 standard that governs how computers handle decimal math.
For everyday math and homework, round half up is almost always what’s expected. If 0.5 rounds to 1 feels right to you, you’re using the right rule for most situations.
How Negative Numbers Work
Rounding negative numbers follows the same distance logic, but the direction can feel counterintuitive. The key is still “which integer is closer?”
Take -3.4. On a number line, it sits between -4 and -3, and it’s closer to -3. So -3.4 rounds to -3. The tenths digit is 4, so the ones place stays the same.
Now take -1.6. It sits between -2 and -1, and it’s closer to -2. So -1.6 rounds to -2. The tenths digit is 6, so you move the ones digit one step further from zero. With negative numbers, “rounding up” in magnitude actually means the number gets more negative: -1.6 becomes -2, not -1.
A quick way to think about it: ignore the negative sign, round normally, then put the negative sign back. Round 1.6 to 2, so -1.6 rounds to -2. Round 3.4 to 3, so -3.4 rounds to -3.
Common Examples
- 4.1 → 4 (tenths digit is 1, round down)
- 4.5 → 5 (tenths digit is 5, round up)
- 4.9 → 5 (tenths digit is 9, round up)
- 12.49 → 12 (tenths digit is 4, round down)
- -0.7 → -1 (tenths digit is 7, round away from zero)
- -5.3 → -5 (tenths digit is 3, stays at -5)
- 99.999 → 100 (tenths digit is 9, round up)
Rounding to Nearest Integer in Spreadsheets
If you’re working in Excel or Google Sheets, the ROUND function handles this directly. The syntax is ROUND(number, num_digits), and when you set num_digits to 0, it rounds to the nearest integer. So =ROUND(3.7, 0) returns 4, and =ROUND(3.2, 0) returns 3.
The INT function in spreadsheets is not the same thing. INT always rounds down (toward negative infinity), so =INT(3.7) returns 3, not 4. If you specifically need the nearest integer, use ROUND with 0 as the second argument.
Rounding to Nearest Integer vs. Other Rounding
Rounding to the nearest integer is just one type of rounding. You might also see instructions to round to the nearest tenth (one decimal place), nearest hundredth (two decimal places), or nearest ten, hundred, or thousand. The logic is identical every time: look at the digit one place to the right of where you’re rounding, and use the 0-4 / 5-9 rule to decide whether to round down or up.
For example, rounding 8,263 to the nearest ten gives 8,260 (the ones digit is 3, so round down). Rounding 8,263 to the nearest hundred gives 8,300 (the tens digit is 6, so round up). The “nearest integer” version of this just means you’re rounding to the ones place, removing all decimal digits.