Rounding and Estimating

1. 1 Write [2 marks]

   Write 7.349 (a) correct to 1 decimal place, (b) correct to 3 significant figures. [2 marks]

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   Model answer

   (a) The next digit is 4, so 7.3. (b) The first three figures are 7, 3, 4, and the next digit 9 rounds the 4 up: 7.35.

   Mark scheme

   • (a) 7.3 — B1
   • (b) 7.35 — B1
2. 2 Write [2 marks]

   Write 0.0705 correct to 2 significant figures. [2 marks]

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   Model answer

   The significant figures are 7 and 0, and the next digit is 5, so round the 0 up: 0.071.

   Mark scheme

   • 0.07 or 0.071 seen — M1
   • 0.071 — A1
3. 3 Estimate [3 marks]

   Calculate an estimate for \(\dfrac{5.9 \times 41}{0.62}\). [3 marks]

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   Model answer

   \(\dfrac{6 \times 40}{0.6} = \dfrac{240}{0.6} = 400\).

   Mark scheme

   • Rounds to 6, 40 and 0.6 — M1
   • \(\dfrac{6 \times 40}{0.6}\) — M1
   • 400 — A1
4. 4 Estimate [3 marks]

   Calculate an estimate for \(\dfrac{18.7 + 31.2}{0.51}\). [3 marks]

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   Model answer

   \(\dfrac{20 + 30}{0.5} = \dfrac{50}{0.5} = 100\).

   Mark scheme

   • Rounds to 20, 30 and 0.5 — M1
   • \(\dfrac{20 + 30}{0.5}\) — M1
   • 100 — A1
5. 5 Write [2 marks]

   Write 45 678 correct to the nearest thousand. [2 marks]

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   Model answer

   The thousands digit is 5, and the next digit 6 rounds it up: 46 000.

   Mark scheme

   • 46 seen — M1
   • 46 000 — A1
6. 6 Estimate [3 marks]

   (a) Calculate an estimate for \(9.8 \times 4.9\). [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) \(10 \times 5 = 50\). (b) Both numbers were rounded up, so the estimate is bigger than the exact value.

   Mark scheme

   • (a) 10 and 5 seen — M1
   • (a) 50 — A1
   • (b) Bigger, because both were rounded up — B1

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.