Rounding Whole Numbers
Rounding is not a rule about the digit 5. It is a question about which of two neighbours you are closer to, and the number line answers it every time.
The two neighbours
Every number sits between two round numbers, and rounding just asks which one it is nearer.
Take 2,400 and round it to the nearest thousand. It lies somewhere between 2,000 and 3,000, and the only question worth asking is which of those two it is closer to. Draw it and the answer arrives before any rule does, which is exactly why the number line is worth using even when a child already knows the trick.
How to round
Three steps, in this order
1. Underline the column you are rounding to.
2. Look at the one digit immediately to its right, and nothing else.
3. If that digit is 5 or more, the underlined digit goes up by one. Otherwise it stays. Everything to the right becomes zero.
Step two is where most marks are lost, so it is worth saying plainly: you look at exactly one digit. Rounding 3,472 to the nearest hundred means looking at the 7 and ignoring the 2 completely, however much it feels like the 2 should get a say.
Round 3,472 to the nearest hundred.
- The hundreds digit is 4, so the two neighbours are 3,400 and 3,500.
- The digit immediately to its right is 7.
- 7 is more than 5, so the 4 goes up to 5.
- Everything after the hundreds column becomes zero.
3,500
Round 48,219 to the nearest thousand.
- The thousands digit is 8, so the neighbours are 48,000 and 49,000.
- The digit to its right is 2.
- 2 is less than 5, so the 8 stays as it is.
- Everything after the thousands column becomes zero.
48,000
Exactly halfway
A number ending in exactly 5 is genuinely the same distance from both neighbours, so no amount of looking at the line will decide it. Someone had to pick, and the agreement is that it goes up. That is not a fact about numbers, it is a convention, and children find it much easier to accept once they are told it is a convention rather than being made to hunt for a reason that is not there.
Say it as a tie-break
"It is a tie, and ties go up." Children who have played any game understand a tie-break rule immediately, and it stops them looking for a mathematical reason that does not exist.
Why anyone rounds
Rounding is not a school exercise invented to fill a worksheet. Nobody says a stadium held 48,219 people, or that a journey took 3,472 metres. We round because the extra digits carry no useful information for the decision being made, and because a number you can hold in your head beats one you cannot.
It is also how you check your own work. If a child multiplies 39 by 21 and gets 189, rounding to 40 times 20 says the answer should be near 800. Something is wrong, and they can see it is wrong without redoing the sum.
Common mistakes
1. Rounding one step at a time, from the right
Rounding 3,449 to the nearest hundred by first making the 9 into a 5, then the 5 into a 4 going up, and arriving at 3,500. Each step looks reasonable and the answer is wrong. You look at one digit, once. 3,449 rounds to 3,400.
2. Leaving the other digits in place
Rounding 3,472 to the nearest hundred and writing 3,572. Everything to the right of the rounded column becomes zero, because that is what rounding means: the smaller detail is being thrown away on purpose.
3. Getting stuck when the digit is a 9
Rounding 1,962 to the nearest hundred, seeing that the 9 has to go up, and stopping. Nine plus one is ten, which will not fit in one column, so it carries exactly the way it does in addition. The answer is 2,000.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
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What to learn next
The same three steps work on decimals, with one extra thing to watch: the digits after the rounded place disappear entirely rather than turning into zeros.
For parents
Next time you are at the till, ask your child to round the total to the nearest dollar before you pay, and then again to the nearest ten. Two questions, ten seconds, and it puts rounding where it actually belongs, which is in estimating rather than in a worksheet.
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