OpenRevise

Exam questions · Maths · Standard Form and Accuracy

Rounding and Estimating

  • 6 exam questions
  • 15 marks
  • 9 quick checks
  1. 1 Write [2 marks]

    (a) Write 4.678 correct to 1 decimal place. (1 mark) (b) Write 4.678 correct to the nearest whole number. (1 mark)

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    Model answer

    (a) The next digit is 7, so \(4.7\). (b) The next digit is 6, so 5.

    Mark scheme

    • (a) 4.7 — B1
    • (b) 5 — B1
  2. 2 Write [2 marks]

    Write 0.004567 correct to 2 significant figures.

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    Model answer

    The first significant figure is 4, the second is 5, and the next digit 6 rounds the 5 up. The answer is 0.0046.

    Mark scheme

    • 0.004 or 0.005 seen, or a correct method — M1
    • 0.0046 — A1
  3. 3 Estimate [3 marks]

    Work out an estimate for \(\dfrac{4.97 \times 20.1}{0.49}\).

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    Model answer

    Round each number to 1 significant figure: \(\dfrac{5 \times 20}{0.5} = \dfrac{100}{0.5} = 200\).

    Mark scheme

    • At least two numbers rounded to 1 s.f., such as 5 and 20 — M1
    • \(\dfrac{5 \times 20}{0.5}\) — M1
    • 200 — A1
  4. 4 Estimate [3 marks]

    Work out an estimate for \(\dfrac{39.8 \times 5.1}{0.21}\).

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    Model answer

    \(\dfrac{40 \times 5}{0.2} = \dfrac{200}{0.2} = 1000\).

    Mark scheme

    • Rounds to 40, 5 and 0.2 — M1
    • \(\dfrac{40 \times 5}{0.2}\) — M1
    • 1000 — A1
  5. 5 Write [2 marks]

    Write 6482 (a) correct to 2 significant figures, (b) correct to the nearest hundred.

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    Model answer

    (a) The first two figures are 6 and 4, and the next digit 8 rounds the 4 up: 6500. (b) The hundreds digit is 4, and the next digit 8 rounds it up: 6500.

    Mark scheme

    • (a) 6500 — B1
    • (b) 6500 — B1
  6. 6 Estimate [3 marks]

    (a) Work out an estimate for \(\dfrac{4.9 \times 9.8}{0.52}\). (2 marks) (b) Is your estimate bigger or smaller than the exact value? Give a reason. (1 mark)

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    Model answer

    (a) \(\dfrac{5 \times 10}{0.5} = 100\). (b) Both numbers on the top were rounded up, and the bottom was rounded down, which makes the fraction bigger. So the estimate is bigger than the exact value.

    Mark scheme

    • (a) \(\dfrac{5 \times 10}{0.5}\) — M1
    • (a) 100 — A1
    • (b) Bigger, with a reason about the rounding — C1

Quick check

  1. 1

    What is 4.678 to 1 decimal place?

    1. A4.6
    2. B4.68
    3. C5
    4. D4.7
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    D: 4.7

    The next digit is 7, so round up.

  2. 2

    What is 6482 to 2 significant figures?

    1. A65
    2. B6400
    3. C6500
    4. D6480
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    C: 6500

    The first two figures are 6 and 4, and the next digit 8 rounds the 4 up to 5, with zeros to hold the place.

  3. 3

    What is 0.004567 to 2 significant figures?

    1. A0.0045
    2. B0.0046
    3. C0.00457
    4. D0.0047
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    B: 0.0046

    The first significant figure is the 4, and the next digit 6 rounds the 5 up.

  4. 4

    What is 83.7 to the nearest 10?

    1. A80
    2. B90
    3. C84
    4. D83
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    A: 80

    83.7 is closer to 80 than to 90.

  5. 5

    What is the best estimate for \(\dfrac{4.97 \times 20.1}{0.49}\)?

    1. A20
    2. B2000
    3. C100
    4. D200
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    D: 200

    \(\dfrac{5 \times 20}{0.5} = \dfrac{100}{0.5} = 200\).

  6. 6

    To estimate a calculation, to how many significant figures do you round each number?

    1. A2
    2. B3
    3. C1
    4. D0
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    C: 1

    One significant figure keeps the arithmetic easy.

  7. 7

    The bottom of a fraction is rounded up. What happens to the estimate?

    1. AIt is larger than the true value
    2. BIt is smaller than the true value
    3. CIt is exactly right
    4. DIt cannot be said
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    B: It is smaller than the true value

    A bigger number on the bottom makes the fraction smaller.

  8. 8

    What is the best estimate for \(\dfrac{39.8 \times 5.1}{0.21}\)?

    1. A1000
    2. B100
    3. C10 000
    4. D400
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    A: 1000

    \(\dfrac{40 \times 5}{0.2} = \dfrac{200}{0.2} = 1000\).

  9. 9

    What is 0.0305 to 2 significant figures?

    1. A0.030
    2. B0.03
    3. C0.0305
    4. D0.031
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    D: 0.031

    The significant figures are 3 and 0. The next digit is 5, so round the 0 up to 1.