Rounding and Estimating

1. 1 Write [2 marks]

   Write 0.0764 (a) correct to 2 decimal places, (b) correct to 2 significant figures. [2 marks]

   Show answerHide answer

   Model answer

   (a) The next digit is 6, so 0.08. (b) The first two significant figures are 7 and 6, and the next digit 4 rounds down: 0.076.

   Mark scheme

   • (a) 0.08 — B1
   • (b) 0.076 — B1
2. 2 Write [2 marks]

   Write 58 700 correct to 1 significant figure. [2 marks]

   Show answerHide answer

   Model answer

   The first figure is 5, and the next digit 8 rounds it up to 6, with zeros to hold the place: 60 000.

   Mark scheme

   • 6 seen — M1
   • 60 000 — A1
3. 3 Estimate [3 marks]

   Work out an estimate for \(\dfrac{6.1 \times 19.7}{0.41}\). [3 marks]

   Show answerHide answer

   Model answer

   \(\dfrac{6 \times 20}{0.4} = \dfrac{120}{0.4} = 300\).

   Mark scheme

   • Rounds to 6, 20 and 0.4 — M1
   • \(\dfrac{6 \times 20}{0.4}\) — M1
   • 300 — A1
4. 4 Estimate [3 marks]

   Work out an estimate for \(\dfrac{298 \times 0.52}{5.1}\). [3 marks]

   Show answerHide answer

   Model answer

   \(\dfrac{300 \times 0.5}{5} = \dfrac{150}{5} = 30\).

   Mark scheme

   • Rounds to 300, 0.5 and 5 — M1
   • \(\dfrac{300 \times 0.5}{5}\) — M1
   • 30 — A1
5. 5 Write [2 marks]

   Write 3.996 correct to 2 decimal places. [2 marks]

   Show answerHide answer

   Model answer

   The next digit is 6, so round the 9 up, which carries: 4.00.

   Mark scheme

   • 4 or 4.0 seen — M1
   • 4.00 — A1
6. 6 Estimate [3 marks]

   (a) Work out an estimate for \(5.2 \times 8.3\). [2 marks] (b) Is your estimate bigger or smaller than the exact value? Give a reason. [1 mark]

   Show answerHide answer

   Model answer

   (a) \(5 \times 8 = 40\). (b) Both numbers were rounded down, so the estimate is smaller than the exact value.

   Mark scheme

   • (a) 5 and 8 seen — M1
   • (a) 40 — A1
   • (b) Smaller, because both were rounded down — Q1

Quick check

1. 1

   What is 4.678 to 1 decimal place?

   1. A4.6
   2. B4.68
   3. C5
   4. D4.7
   Show answerHide answer

   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
   Show answerHide answer

   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
   Show answerHide answer

   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
   Show answerHide answer

   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
   Show answerHide answer

   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
   Show answerHide answer

   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
   Show answerHide answer

   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
   Show answerHide answer

   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
   Show answerHide answer

   D: 0.031

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