By rounding each number to 1 significant figure, put a ring around the best estimate for 612 x 0.48
A) 600
B) 300
C) 1200
D) 30
(Total for Question 2 is 1 mark)
3
By rounding each number to 1 significant figure, work out an estimate for 78 x 213
(Total for Question 3 is 2 marks)
4
By rounding each number to 1 significant figure, work out an estimate for 5187 / 51
(Total for Question 4 is 2 marks)
5
By rounding each number to 1 significant figure, work out an estimate for 411 x 0.52
(Total for Question 5 is 2 marks)
6
By rounding each number to 1 significant figure, work out an estimate for (39.4 + 58.9) / 9.7
(Total for Question 6 is 3 marks)
7
Nadia buys 48.6 litres of petrol at £3.15 per litre. By rounding each number to 1 significant figure, estimate the total cost.
(Total for Question 7 is 2 marks)
8
Put a ring around the best estimate for √83
A) 8
B) 9
C) 10
D) 7
(Total for Question 8 is 1 mark)
9
Without using a calculator, estimate the value of √146. Show working to support your answer.
(Total for Question 9 is 2 marks)
10
By rounding to 1 significant figure, work out an estimate for 3.872
(Total for Question 10 is 2 marks)
11
By rounding each number to 1 significant figure, work out an estimate for (6.2 x 19.8) / 3.9
(Total for Question 11 is 3 marks)
12
Tom uses his calculator to work out 68 x 297. His calculator shows 2019.6. Use estimation to determine whether Tom's answer is correct, and give an estimate for the correct answer.
(Total for Question 12 is 3 marks)
13
A recipe for 8 people uses 3.85 kg of flour. By rounding suitable values to 1 significant figure, estimate the amount of flour needed for 31 people.
(Total for Question 13 is 3 marks)
14
James is organising a coach trip for 187 people. Each coach holds 48 seats. By rounding both numbers to 1 significant figure, find an estimate for the number of coaches needed.
(Total for Question 14 is 2 marks)
15
By rounding each number to 1 significant figure, put a ring around the best estimate for 0.0038 x 512
A) 2
B) 0.2
C) 20
D) 200
(Total for Question 15 is 2 marks)
16
A train travels at an average speed of 68 km/h for 3.9 hours. By rounding each number to 1 significant figure, estimate the distance travelled.
(Total for Question 16 is 2 marks)
17
By rounding each number to 1 significant figure, put a ring around the best estimate for 0.612 / 0.19
A) 3
B) 30
C) 0.3
D) 6
(Total for Question 17 is 1 mark)
18
Explain why rounding 148 to 1 significant figure gives 100, and not 150.
(Total for Question 18 is 2 marks)
19
By rounding each number to 1 significant figure, estimate the value of 82 x 53. State, giving a reason, whether your estimate is an overestimate or an underestimate of the exact answer.
(Total for Question 19 is 3 marks)
20
By rounding suitable values to 1 significant figure, estimate the value of 58.72 / √83
(Total for Question 20 is 4 marks)
21
By rounding each number to 1 significant figure, estimate the value of (6.9 x 103) x (3.8 x 10-5). Give your answer in standard form.
(Total for Question 21 is 3 marks)
22
A caterer is planning a wedding for 187 guests. Each guest is served a three-course meal costing £9.80 for the starter, £18.60 for the main course and £6.40 for the dessert. The caterer also charges a fixed service fee of £480. By rounding suitable values to 1 significant figure, estimate the total amount the caterer will charge.
(Total for Question 22 is 4 marks)
Mark scheme · 3.3 Estimating
Question 1
(a) B1 700 cao
(a) Answer: 700
(b) B1 0.05 cao
(b) Answer: 0.05
(c) B1 5 cao
(c) Answer: 5
(d) B1 100 cao
(d) Answer: 100
Question 2
B1 B (600 x 0.5 = 300)
Answer: B) 300
Question 3
M1 rounding both values to 1 sf, 80 and 200
A1 16000 cao
Answer: 16000
Question 4
M1 rounding both values to 1 sf, 5000 and 50
A1 100 cao
Answer: 100
Question 5
M1 rounding both values to 1 sf, 400 and 0.5
A1 200 cao
Answer: 200
Question 6
M1 rounding all three values to 1 sf: 40, 60 and 10
M1 dep, (40 + 60) / 10 with correct order of operations
A1 10 cao
Answer: 10
Question 7
M1 rounding both values to 1 sf, 50 and 3
A1 150 (£150) cao
Answer: £150
Question 8
B1 B (92 = 81 is close to 83)
Answer: B) 9
Question 9
M1 identifying 144 = 122 (or 144 < 146 < 169) as the nearest square number
A1 12 (accept 12.0 to 12.2 oe)
Answer: 12
Question 10
M1 rounding 3.87 to 1 sf, 4
A1 16 cao
Answer: 16
Question 11
M1 rounding all three values to 1 sf: 6, 20 and 4
M1 dep, (6 x 20) / 4 with correct order of operations
A1 30 cao
Answer: 30
Question 12
M1 rounding both values to 1 sf, 70 and 300
M1 dep, 70 x 300 = 21000
B1 correct conclusion with reason, e.g. 2019.6 is not close to the estimate of 21000 (about 10 times too small), so Tom's answer is wrong, ft their estimate
Answer: Estimate = 21000; Tom's answer of 2019.6 is wrong (probably a misplaced decimal point).
Question 13
M1 rounding 3.85 to 4 and 31 to 30
M1 dep, 4 x (30 / 8)
A1 15 (kg), awrt 15
Answer: 15 kg
Question 14
M1 rounding both values to 1 sf, 200 and 50
A1 4 cao
Answer: 4 coaches
Question 15
M1 rounding both values to 1 sf, 0.004 and 500
A1 A (2) cao
Answer: A) 2
Question 16
M1 rounding both values to 1 sf, 70 and 4
A1 280 (km) cao
Answer: 280 km
Question 17
B1 A (0.6 / 0.2 = 3)
Answer: A) 3
Question 18
B1 identifying that the first significant figure is the hundreds digit, 1, and all following digits become 0 for 1 sf
B1 correct reasoning that the next digit (4, the tens digit) is less than 5, so the 1 is not rounded up, giving 100; 150 is not a rounding to 1 significant figure
Answer: 100, because the first significant figure (1) is followed by a 4, which is less than 5, so it rounds down; 150 has two significant figures, not one.
Question 19
M1 rounding both values to 1 sf, 80 and 50
A1 4000 cao
B1 underestimate, with reason that both 82 and 53 were rounded down, so the estimate is smaller than the exact answer
Answer: 4000; underestimate
Question 20
M1 rounding 58.7 to 60 and squaring, 602 = 3600
M1 identifying 81 = 92 as the nearest square number to 83, so √83 is approximately 9
M1 dep, 3600 / 9
A1 400 cao
Answer: 400
Question 21
M1 rounding both values to 1 sf, 7 and 4
M1 dep, 7 x 4 = 28 with powers of 10 combined, 103 x 10-5 = 10-2
A1 2.8 x 10-1 cao (accept 0.28)
Answer: 2.8 x 10-1
Question 22
M1 finding the cost per guest, 9.80 + 18.60 + 6.40 = 34.80
M1 rounding to 1 sf: 34.80 to 30, 187 to 200, and 480 to 500