Topics · Primary Maths · Rounding & Estimation
Rounding and estimating
Rounding replaces a number with a nearby simpler one. Estimating uses rounded numbers to get a rough answer fast — which is how you catch a careful answer that has gone badly wrong.
- 86 exam papers analysed
- appears in 58% of P4 Maths papers
- ~3 min read
01 Rounding is choosing the nearer one
To round 4,507 to the nearest hundred, ask which hundred it is nearer to: 4,500 or 4,600. It is nearer to 4,500.
The shortcut is to look at the digit after the place you are rounding to. 5 or more rounds up; less than 5 rounds down. Here that digit is the 0 in the tens, so it rounds down.
Everything after the rounding place becomes zero. 4,507 to the nearest hundred is 4,500, not 4,507 with a note attached.
02 The halfway rule
4,550 is exactly halfway between 4,500 and 4,600, so “nearer” does not decide it. The agreed rule is to round up, giving 4,600.
It is a convention rather than a fact, adopted so that everyone gets the same answer. That is worth saying plainly, because children reasonably ask why.
03 Estimating to check
An estimate is a rough answer from rounded numbers, and its job is to catch the careful answer that is wildly wrong — a misplaced digit, a forgotten carry, an operation done backwards.
- Round each number to something easy to work with.
- Do the sum with the rounded numbers, in your head.
- Compare. 4,507 + 2,896 is roughly 4,500 + 2,900 = 7,400. A careful answer of 7,403 is believable; 1,611 or 74,030 is not.
- An estimate is never the final answer unless the question asked for one. It is a check.
04 When it says “estimate”
If a question asks you to estimate, the rounded answer is what it wants. Working it out exactly and then rounding at the end is answering a different question, and papers do notice.
Round first, then calculate. That is what makes it an estimate rather than a rounded exact answer.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- roundmore than one—
To replace a number with a nearby simpler one, to the nearest ten, hundred and so on.
- estimatesayES-ti-maytmore than oneestimates
A rough answer worked out from rounded numbers.
- approximatelysayuh-PROK-si-muht-lee
Roughly, about. Written with the sign ≈.
- nearest
The rounding place a question names: to the nearest 10, 100, 1,000 or whole number.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P4
Rounding to the nearest 10, 100 and 1,000, and estimating to check a calculation.
Practise P4 Rounding & Estimation — 10 questions →58% of P4 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“4,507 to the nearest hundred is 4,600, because the 7 rounds up.”
Look at the digit after the hundreds, which is the 0 in the tens. Zero is less than 5, so it rounds down to 4,500.
“4,550 rounds down because it is not past halfway.”
It is exactly halfway, and the agreed rule is to round up: 4,600.
“Round 4,507 to the nearest hundred: 4,507 → 4,500 → 4,000.”
Round once, to the place asked for. Rounding again to the nearest thousand answers a different question.
“It said estimate, so I worked it out exactly and then rounded.”
Round first, then calculate. Otherwise it is a rounded exact answer, not an estimate.
“My estimate was 7,400 so I wrote that as the answer.”
Only if the question asked for an estimate. Otherwise it is a check on the exact answer, not a replacement for it.
Now try it
10 questions across 1 levels, marked as you go with the working shown.