Rounding Calculator
Enter a number and what to round it to. It gives the answer and names the digit that decided which way it went.
Rounded
4,800
- Rounded
- 4,800
- Started at
- 4,763
- To the nearest
- 100
- Deciding digit
- 6
- The deciding digit is 6, which is 5 or more, so it rounds up.
- Look only at the digit immediately below the place you are rounding to. Everything after it is irrelevant — 4,749 rounds to 4,700 because the deciding digit is 4, even though 49 is nearly 50.
- Five rounding up is a convention rather than a rule of arithmetic. It is exactly halfway, so either answer is equally close; rounding up is simply what everyone agreed to do, and it is what a marker will expect.
About rounding
Rounding replaces a number with a nearby one that is easier to work with. The question is always the same: of the two multiples on either side, which is closer?
The method is to look at one digit — the one immediately below the place you are rounding to. If it is 5 or more, round up; if it is less than 5, round down. That digit is the only one that matters, which is the part most often got wrong.
Rounding 4,749 to the nearest hundred is the classic trap. The deciding digit is the 4 in the tens column, so it rounds down to 4,700 — even though 49 feels close to 50. Looking at 49 and rounding it to 50 first, then rounding again, gives 4,800 and is wrong. Round once, from the original number.
Five rounding up is a convention rather than a rule of arithmetic. Exactly halfway is exactly halfway, and either answer is equally close; rounding up is simply what everyone agreed to do, and it introduces a very slight upward bias that statisticians sometimes avoid with other schemes. For schoolwork, five goes up.
What it works out
- To the nearest ten, hundred, thousand or million
- To a decimal place
- The digit that decided it
- Which way it went, and why
The formula
Look at the digit below the place you want. 5 or more rounds up; less than 5 rounds down.
Rounding 4,763 to the nearest hundred means choosing between 4,700 and 4,800.
The place being rounded to is the hundreds, so the deciding digit is the one immediately below it — the 6 in the tens column. Six is 5 or more, so it rounds up, and the answer is 4,800.
Everything below the deciding digit is ignored completely. That is why 4,749 rounds to 4,700: the deciding digit is 4, and the 9 after it has no say. Rounding the 49 up to 50 first and then rounding again gives 4,800, which is a real and common mistake — round once, from the number you started with.
Rounding to a decimal place works identically, just further right. To one decimal place, 4.56 has a deciding digit of 6 in the hundredths, so it rounds up to 4.6.
- Deciding digit
- The one immediately below the place you are rounding to. Nothing after it counts.
- Rounds up
- The deciding digit is 5, 6, 7, 8 or 9.
- Rounds down
- The deciding digit is 0, 1, 2, 3 or 4.
A worked example
4,763 rounded to the nearest hundred.
That works out to 4,800 .
- Rounded
- 4,800
- Started at
- 4,763
- To the nearest
- 100
- Deciding digit
- 6
Questions
How do you round to the nearest hundred?
Look at the tens digit. If it is 5 or more round up, otherwise round down. 4,763 has a 6 in the tens, so it rounds up to 4,800.
Does 5 round up or down?
Up, by the usual convention. It is exactly halfway so either would be equally close, and rounding up is simply the agreed rule — and what a marker will expect.
What does 4749 round to, to the nearest hundred?
4,700. The deciding digit is the 4 in the tens column, and the 9 after it does not count. Rounding the 49 to 50 first and then rounding again gives 4,800 and is wrong.
Why do we only look at one digit?
Because that digit alone settles which side of halfway the number falls. Once you know the tens digit is 4, the number is below 4,750 whatever comes after it, so 4,700 is closer.
How do I round to a decimal place?
The same way, further right. For one decimal place look at the hundredths digit: 4.56 rounds to 4.6, and 4.54 rounds to 4.5.
What is the difference between rounding and truncating?
Truncating just chops the extra digits off, so 4.99 truncates to 4. Rounding picks the nearest value, so 4.99 rounds to 5. Truncating always goes down and is not the same thing.
Why does rounding matter?
It makes numbers easier to hold in your head and to estimate with. Checking that an answer is roughly right — 4,800 rather than 48,000 — catches far more mistakes than re-reading the working does.
What happens when rounding up changes every digit?
It carries, exactly like addition. 997 to the nearest ten is 1,000, because rounding the 7 up pushes the 9s over as well.