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Academy11+

11+ Maths · Topic explained

Rounding and estimating

How can you check 398 × 21 in your head in two seconds?

The big idea

Rounding swaps a number for the nearest tidy number, so you can estimate quickly.

Picture it

Put the number on a number line: it moves to whichever tidy number is nearer. Halfway (5) goes up.

Key words

round
Change a number to the nearest 10, 100, 1,000 or whole number.
estimate
A sensible answer worked out with rounded numbers.
approximately (≈)
About, nearly equal to.
decimal place
A digit after the decimal point: 1 d.p. keeps the tenths.

Worked examples

  1. 1Warm-up

    Round 47 to the nearest 10

    • 47 is between 40 and 50
    • It is 3 from 50 but 7 from 40
    • So 47 rounds to 50
  2. 211+ standard

    Round 3.846 to 1 decimal place

    • Keep the tenths: 3.8 | 46
    • The next digit is 4, less than 5, so round down
    • 3.846 ≈ 3.8
  3. 311+ standard

    Estimate 398 × 21

    • 398 ≈ 400 and 21 ≈ 20
    • 400 × 20 = 8,000
    • (The exact answer is 8,358: close!)
  4. 411+ standard

    Round 6,950 to the nearest hundred

    • 6,950 is exactly halfway between 6,900 and 7,000
    • Halfway rounds up
    • 6,950 ≈ 7,000

The common mistake

The mistake

Round 3.846 to 1 d.p. in stages: 3.846 → 3.85 → 3.9.

Instead

Look only at the digit straight after the place you keep: 3.8|46 → 3.8.

Why: Rounding in stages pushes numbers up that should go down.

Where it comes up in the 11+

Rounding to 10, 100, 1,000 or decimal places, and estimating to check an answer or pick the likely option.

The video

Video coming soon

We're making a short video that explains rounding and estimating step by step. Until then, everything it covers is on this page.

Free printable

Rounding and estimating worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Round 7,481 to the nearest thousand.

    • 7,000
    • 7,500
    • 8,000
    • 7,480
    Show the answer

    7,000

    The hundreds digit is 4, so round down.

  2. 2. What is the smallest whole number that rounds to 300 to the nearest 10?

    • 290
    • 294
    • 295
    • 299
    • 305
    Show the answer

    295

    295 is halfway between 290 and 300, so it rounds up; 294 rounds down to 290.

  3. 3. Which is the best estimate of 51 × 19?

    • 100
    • 700
    • 1,000
    • 10,000
    Show the answer

    1,000

    51 ≈ 50 and 19 ≈ 20, and 50 × 20 = 1,000.