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Rounding strategies

To the nearest 10, 100, 1000 or whole number, and to 1 or 2 decimal places.

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Sometimes we don’t need an exact number. “About 300 children” is quicker to say than “297 children”, and it is close enough.

Rounding means swapping a number for a nearby tidy number. In this lesson you will learn:

  • how to round to the nearest 10, 100 and 1000
  • how to round a decimal to the nearest whole number
  • how to round to 1 or 2 decimal places
  • the one rounding mistake to watch out for
  • how to work backwards from a rounded number

1. What rounding means

Key idea Round to the nearest tidy number. If a number is exactly halfway, it rounds up.

Picture a hill with a tidy number at each foot. Put your number on the hill and let it go. It rolls down to the side it is on.

  • On the left side of the top: it rolls back to the smaller number. We round down.
  • On the right side: it rolls on to the bigger number. We round up.
  • Exactly on the top: it always rolls forward. Halfway rounds up.

Round 4,649 to the nearest 100.

round down round up halfway: 4,650 4,600 4,700 4,649

4,649 is on the left side of the hill, so it rolls down to 4,600. 4,649 rounded to the nearest 100 is 4,600.

2. The decider digit

Key idea Look at the digit just to the right of the column you are rounding to. It is the decider. 5 or more: round up. 4 or less: round down.

How to round

  1. Find the column you are rounding to
    To the nearest 100? Find the hundreds digit.
  2. Look at the decider: the digit just to its right
  3. 5 or more? Add 1 to your digit. 4 or less? Keep it the same.
  4. Every digit after it becomes 0
    For decimals, the digits after it are simply left off (Section 4).

Example 1: round 6,847 to the nearest 100

6,847

  • The hundreds digit is 8. The decider is 4.
  • 4 is less than 5, so the 8 stays. The 4 and 7 become 0s.
Answer6,800

Example 2: round 3,962 to the nearest 100

3,962

  • The hundreds digit is 9. The decider is 6, so round up.
  • 9 hundreds plus 1 hundred is 10 hundreds, which is 1 thousand. So 3 thousands become 4 thousands.
Answer4,000

3. Rounding to 10, 100, 1000 and whole numbers

Key idea The same number rounds differently depending on what you round to.
Round 45,368 to the nearestDeciderAnswer
108 (round up)45,370
1006 (round up)45,400
10003 (round down)45,000

To round a decimal to the nearest whole number, the decider is the tenths digit. 7.6 rounds to 8. 7.4 rounds to 7. 7.5 is halfway, so it rounds up to 8.

4. Rounding to 1 or 2 decimal places

Key idea Decimal places are the digits after the point. 1 decimal place means keep 1 digit after the point. 2 decimal places means keep 2.
  • Round to 1 decimal place: you are rounding to the nearest tenth. The decider is the hundredths digit.
  • Round to 2 decimal places: you are rounding to the nearest hundredth. The decider is the thousandths digit.

Example: round 3.462

3.462

  • To 1 decimal place: keep the 4, the decider is 6, so round up: 3.5
  • To 2 decimal places: keep the 4 and 6, the decider is 2, so round down: 3.46
Watch out 2.97 to 1 decimal place is 3.0, not 3. The 9 tenths rounds up to 10 tenths, which is 1 whole. Keep the 0: it shows you rounded to 1 decimal place.

Try the rounding hill in Section 1 with 1 d.p. and 2 d.p. to see it work for decimals.

5. The mistake to avoid: round once

Key idea Always round from the number you were given, in one step.

Example: round 4,649 to the nearest 100

Wrong: rounding in steps 4,649 → 4,650 → 4,700
Right: round once The decider is 4, so round down: 4,600

Rounding to 4,650 first moved the number up a little, and that tipped it over the top of the hill. The ball at 4,649 really is on the left side.

6. Working backwards

Key idea Lots of numbers round to the same answer. They sit between the two halfway points either side of it.

Example: a whole number rounds to 4,600 (nearest 100). What could it be?

  • The halfway point below 4,600 is 4,550. That rounds up to 4,600, so it counts. It is the smallest.
  • The halfway point above is 4,650. That rounds up to 4,700, so it does not count. The largest is 4,649.
Answerany whole number from 4,550 to 4,649

The mistakes that cost marks

  1. Rounding in steps. 4,649 is not 4,700 to the nearest 100. round once, from the number you were given: 4,600.
  2. Looking at the wrong digit. the decider is the digit just to the right of the column you are rounding to.
  3. Rounding 5 down. 350 to the nearest 100 is not 300. remember halfway always rounds up: 400.
  4. Forgetting the zeros. 6,847 to the nearest 100 is not 68. fill every column after your digit with 0: 6,800.
  5. Forgetting to carry. 3,962 to the nearest 100 is not 3,000. 10 hundreds make 1 thousand: 4,000.
  6. Dropping the 0 in a decimal answer. 2.97 to 1 decimal place is not 3. write 3.0, to show 1 decimal place.

Quick checklist

Tick each one when you can do it without help.

Download

Print these and work through them away from the screen.

Year 4 practice paper PDF · 11+ style, with answer sheet and answers Year 5 practice paper PDF · 11+ style, with answer sheet and answers Year 6 practice paper PDF · 11+ style, with answer sheet and answers

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