Rounding
Rounding replaces a number with the landmark nearest to it. 38 becomes 40 because it is two steps from forty and eight steps from thirty, and that quick judgement is what makes estimating possible.
The rounding tool
Where does it fall on the line?
Drag the marker, or use the arrow keys
38 40
Find the marker on the line.
How rounding works
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Find the two landmarks either side
Every number sits between two tens. Thirty-eight is past thirty and not yet forty, so those are the only two candidates. The number line on this page shows that gap, and dragging the marker along it makes the two landmarks obvious.
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Measure which is nearer
Thirty-eight is 8 from thirty and 2 from forty, so it rounds to 40. When a number lands exactly halfway, at 35 or 45, the world has agreed to round up: 35 becomes 40. The shortcut is to read the ones digit — 0 to 4 rounds down, 5 to 9 rounds up.
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Use the estimate to check the exact answer
Estimating 38 + 31 as 40 + 30 gives about 70, and the exact answer of 69 sits right next to it. That is what estimates are for: they are not the answer, they are the guard rail that tells you an answer of 96 must have gone wrong.
Worked examples
38 → ?
Forty. Thirty-eight sits between 30 and 40, two steps from forty and eight from thirty, so the nearer ten is 40. The ones digit is 8, which is 5 or more, so the tens digit moves up.
35 → ?
Forty. Thirty-five is exactly halfway, five from each ten. The rule everyone uses is that halfway rounds up, so 35 becomes 40. It is a convention rather than a mathematical law, but it is the one to learn because it keeps answers consistent.
47 + 32 ≈ ?
About 80. Rounding first: 47 is nearer 50 and 32 is nearer 30, so 50 + 30 = 80. The exact answer is 79, which is close enough to trust — if a method had produced 89, the estimate would have caught it.
Where it goes wrong
- Rounding the wrong digit In 462, the ones digit is 2, but rounding to the nearest ten uses the tens digit: 462 is nearer 460 than 470. Choosing which digit to look at is most of the skill, and it is worth saying the target out loud first.
- Rounding 34 by chopping the digit off Chopping gives 3, which is a hundred times too small. Rounding never deletes the number — it replaces it with a nearby landmark that has the same size, so 34 rounds to 30, not 3.
- Treating an estimate as the answer An estimate of 70 for 38 + 31 is not the sum; the sum is 69. Estimating is a way of checking, and a learner who writes ≈ when they should write = is answering a slightly different question.
Questions
What does rounding actually do?
It swaps a number for the nearest landmark number, so that a fiddly amount becomes easy to work with. Rounding 38 to 40 keeps the size of the number roughly intact while making it simple to add, subtract or multiply in your head.
Is 35 rounded to 40 or to 30?
To 40. Thirty-five is exactly halfway, and by convention halfway rounds up. You can remember it as "five and above, give it a shove". The convention exists so that everyone rounding the same number gets the same answer, which matters as soon as rounding is used to check work or compare prices.
Is a rounded answer wrong?
It is a different question: 38 rounded to the nearest ten is 40, and that is not claiming 38 equals 40. When an answer is rounded rather than exact it is written with the ≈ sign, which means "is approximately". An estimate that is treated as exact is where errors creep in.
How do I round to the nearest hundred?
Exactly the same way, one place further left. Find the hundreds either side and see which is nearer: 462 sits between 400 and 500, and it is 62 from 400 and 38 from 500, so it rounds to 500. The shortcut is to look at the tens digit, since it decides how far past the last hundred you are.
Why bother estimating when I can work it out exactly?
Because an estimate is nearly free and it catches the answer that is wildly wrong. Estimating 38 + 31 as about 70 means an answer of 96 stands out immediately, before a long method has been checked line by line. Estimating first also makes written methods less intimidating, because you already know roughly what is coming.