Rounding replaces a number with a simpler one that is close to it, keeping only the precision you need: a price to the nearest cent, a distance to the nearest mile, a population to the nearest thousand. This calculator rounds to any place value from the millions down to the millionths, highlights the digit you are rounding and the digit that decides which way to go, and lists the same number rounded to every other place for comparison.
How to use the rounding calculator
- Type the number. Commas, decimals and negative signs are all accepted.
- Choose the place to round to — for example Tens, Ones (whole number), Tenths or Hundredths.
- The result appears on the tape. The digit display marks the rounding digit in blue and the deciding digit in amber, and the table shows the number rounded to every other place.
The rounding rule
Every place-value rounding problem follows the same three steps:
- Find the digit in the place you are rounding to.
- Look at the digit just to its right — the deciding digit.
- Decide: if the deciding digit is 5, 6, 7, 8 or 9, add 1 to the rounding digit. If it is 0, 1, 2, 3 or 4, leave the rounding digit as it is. Then drop all digits to the right (after a decimal point) or replace them with zeros (in a whole number).
Only the one digit to the right matters. When rounding 3.449 to the nearest tenth, the deciding digit is the 4 in the hundredths place, so the answer is 3.4 — even though the 9 further along might tempt you to round twice. Rounding in stages (3.449 → 3.45 → 3.5) is a classic error.
Worked example
Round 4,827.3651 to the nearest hundredth.
Rounding digit: the hundredths digit is 6 (4,827.3651)
Deciding digit: the thousandths digit is 5
Decide: 5 is 5 or more, so the 6 becomes 7
Drop the rest: 4,827.37
The same number rounded to other places:
| Nearest | Result |
|---|---|
| Thousand | 5,000 |
| Hundred | 4,800 |
| Ten | 4,830 |
| Whole number | 4,827 |
| Tenth | 4,827.4 |
| Hundredth | 4,827.37 |
| Thousandth | 4,827.365 |
Place values to round to
| Place | Example: 58,316.2794 |
|---|---|
| Ten thousands | 60,000 |
| Thousands | 58,000 |
| Hundreds | 58,300 |
| Tens | 58,320 |
| Ones | 58,316 |
| Tenths | 58,316.3 |
| Hundredths | 58,316.28 |
| Thousandths | 58,316.279 |
Not sure which place a digit sits in? The place value calculator labels every digit of a number.
Special cases
Carrying when you round up a 9
If the rounding digit is 9 and you round up, it becomes 10: write 0 and carry 1 to the left, just as in addition. 6.97 rounded to the nearest tenth is 7.0, and 49,960 rounded to the nearest hundred is 50,000.
Rounding money
Dollar amounts round to the nearest cent, which is the hundredths place. A $19.996 unit price shows as $20.00; a 7.25% sales tax on $13.49 is $0.978025, which rounds to $0.98.
Negative numbers
This calculator rounds by size and keeps the sign, so −2.5 becomes −3. Some software rounds ties differently — toward positive infinity or to the nearest even digit. The rounding methods calculator compares ten different rules side by side.
Rounding vs. significant figures
Rounding to a place keeps a fixed number of decimal places no matter how large or small the number is. Rounding to significant figures keeps a fixed number of meaningful digits, which is standard in science. For that, use the significant figures rounding calculator. To round to the nearest 5, 25 or quarter instead of a power of ten, use the round to nearest multiple calculator.
Frequently asked questions
How do you round a number to a given place?
Find the digit in that place, then look at the digit immediately to its right. If that digit is 5 or more, add 1 to the place digit; if it is 4 or less, leave the place digit alone. Finally drop the digits after a decimal place, or turn them into zeros for whole-number places.
What is 4,827.3651 rounded to the nearest hundredth?
The hundredths digit is 6 and the digit after it is 5, so round up to 4,827.37.
What happens when I round up a 9?
The 9 becomes 10, so you write 0 and carry 1 into the place to its left. Rounding 999.96 to the nearest tenth gives 1,000.0.
How do I round negative numbers?
Round the size of the number and keep the minus sign. −2.5 rounds to −3 and −4.42 rounds to −4.4. This is called rounding half away from zero and is what most schools teach.
Should I keep trailing zeros after rounding?
Yes, if they show the place you rounded to. 12 rounded to the nearest hundredth is written 12.00, and 999.96 rounded to the nearest tenth is 1,000.0. The zeros tell the reader how precise the number is.