Estimation and Rounding

Updated 7 October 2026

Knowing the size of an answer before you work it out is what catches a slipped decimal point: you expected about 2,000, the calculator says 19,760, and the gap between them is the warning.

How do you round a whole number?

To round a whole number, find the place you are rounding to and look at the one digit just to its right: 5 or more rounds up, 4 or less rounds down. To round 62 to the nearest ten, the tens on either side are 60 and 70, and the ones digit is 2, so 62 rounds down to 60. The rule works because it picks the nearer of the two tens: 62 is 2 away from 60 and 8 away from 70. A number ending in 5 sits exactly halfway, so by convention it rounds up, and 65 becomes 70. Hundreds and thousands use the same rule one place further left: 2,741 to the nearest hundred looks at the tens digit, 4, and becomes 2,700. Watch for a 9 that rounds up and carries: 596 to the nearest ten becomes 600. To check, the answer should be no more than half a step from the start.

To the nearest ten: one digit decides

1. Find the tens on either side. (For 47: 40 and 50.)
2. Look at the ones digit only. 5 or more $\to$→ up. 4 or less $\to$→ down.

$47\to 50$47 → 50. $43\to 40$43 → 40. $45\to 50$45 → 50 (halfway rounds up).

To the nearest hundred or thousand: same rule, one place along

The digit one place to the right of the target decides — and only that digit.

1,860 to the nearest hundred $\to$→ the tens digit is $6\to 1$6 → 1,900.

3,485 to the nearest thousand $\to$→ the hundreds digit is $4\to 3$4 → 3,000. (Yes, down — the 85 does not get a vote.)

Rounding decimals: the same rule again

4.56 to one decimal place $\to$→ next digit $6\to 4.6$6 → 4.6. 7.43 to the nearest whole $\to$→ next digit $4\to 7$4 → 7.

More on decimal places in the decimals guide.

How do you estimate a calculation?

To estimate a calculation, round each number to a friendly value, usually its first digit and zeros, do the easy calculation, and give the answer as about that much. For 63 × 28, round to 60 × 30 = 1,800, so the answer is about 1,800. The exact answer is 63 × 28 = 1,764, so an answer of 17,640 or 176 shows a slipped digit. It works because small changes to the numbers make a small change to the answer, and friendly numbers leave a times-table fact with zeros. In a product, the case to watch is rounding both numbers the same way, which stacks the errors. Round one up and one down, as 63 went down and 28 went up here, and the errors partly cancel. For a sum, the nearest hundred is usually enough: 412 + 297 is about 400 + 300 = 700. To check an estimate, count the zeros: 6 × 3 = 18, and two zeros make 1,800.

Step by step

1. Round each number to one friendly digit (its front digit, usually).
2. Do the now-easy calculation in your head.
3. Say the answer with an honest "about".

$38\times 52\approx 40\times 50=2$38 × 52 ≈ 40 × 50 = 2,000 (true answer 1,976 — within about 1%).

$487+512\approx 500+500=1$487 + 512 ≈ 500 + 500 = 1,000 (true answer 999).

The professional touch: one up, one down

38 × 52 rounds 38 up to 40 and 52 down to 50, which is why the estimate lands so close.

Sanity checks: what size should the answer be?

Before accepting any careful answer, ask what size it should be. A restaurant bill of $87 split four ways should be "a bit over $20 each" — if long division hands you $217.50, the estimate catches it instantly. This works on units too: a door 2 meters tall is plausible; a door 2 centimeters tall is a cat flap for a mouse.

How is rounding to compute different from estimating?

Rounding to compute gives an exact answer, while estimating gives an approximate one. Both round to a friendly number, but rounding to compute pays back the difference. To work out 256 + 98, add 100 instead of 98, then take away the extra 2: 256 + 100 − 2 = 354. That answer is exact. An estimate of the same sum rounds and stops: 256 + 98 is about 250 + 100 = 350, which gives the size but not the answer. Rounding and adjusting works because 98 is 2 less than 100, so adding 100 and taking 2 away adds exactly 98. In subtraction the adjustment turns around: to take away 98, take away 100 and then add 2 back, so 256 − 98 = 256 − 100 + 2 = 158. To check an adjusted answer, compare it with the estimate: 354 is close to 350, while a slip such as 454 is not.

$348+99\to 348+100-1=447$348 + 99 → 348 + 100 − 1 = 447. Exact, not an estimate.

A word on significant figures

Later on, "round to the nearest hundred" grows up into "round to 2 significant figures" — counting digits from the first nonzero one, so 0.004718 to 2 s.f. is 0.0047. Same deciding-digit rule, new way of naming the cut. The app's Significant Figures lesson takes it from there.

The three mistakes worth naming

• Letting far-right digits vote. 3,485 to the nearest thousand is 3,000 — the 85 cannot drag it across halfway.
• Rounding both numbers the same way in a product. Errors stack; go one up, one down.
• Serving an estimate as exact. $\approx$≈ earns its keep by being honest — 40 × 50 tells you 1,976 is plausible, not that it is 2,000.