Estimation (Copy)
Practice Questions — 1.9 Estimation
Question 1
Round 5764:
(a) to the nearest thousand
(b) to the nearest hundred
(c) to 2 significant figures
Question 2
Round the following to 3 significant figures:
(a) 0.004527
(b) 82349
(c) 5.6782
Question 3
Round the following to 2 decimal places:
(a) 7.836
(b) 15.097
(c) 0.004382
Question 4
Estimate the value of 397 × 62 by rounding each number to 1 significant figure.
Question 5
Estimate the value of 892 ÷ 297 by rounding each number to 1 significant figure.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
Round 0.000973 to:
(a) 1 significant figure
(b) 2 significant figures
(c) 3 significant figures
Question 7
A length is measured as 12.486 cm.
Round this to:
(a) 1 decimal place
(b) 2 decimal places
(c) 3 significant figures
Question 8
Estimate the value of 498 ÷ 0.052 by rounding to 1 significant figure.
Question 9
Estimate the value of √38 × 0.412 by rounding both numbers to 1 significant figure.
Question 10
Round each of the following to the nearest whole number:
(a) 3.49
(b) 8.51
(c) 12.5
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
The population of a city is 8 496 325. Round this to:
(a) the nearest million
(b) the nearest hundred thousand
(c) 2 significant figures
Question 12
Estimate 47 × 191 by rounding each number to 1 significant figure.
Question 13
Round 0.0007648 to:
(a) 1 significant figure
(b) 2 significant figures
Question 14
Estimate the value of 628 × 51 ÷ 302 by rounding each number to 1 significant figure.
Question 15
Round each of the following to 2 significant figures:
(a) 0.009382
(b) 78541
(c) 63.287
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 1.9 Estimation
1.
(a) 5764 → 6000 (nearest thousand)
(b) 5764 → 5800 (nearest hundred)
(c) 5764 → 5800 (2 significant figures)
Explanation: Round based on the digit after the required place value.
2.
(a) 0.004527 → 0.00453 (3 s.f.)
(b) 82349 → 82300 (3 s.f.)
(c) 5.6782 → 5.68 (3 s.f.)
Explanation: Keep first 3 non-zero digits, round the next digit.
3.
(a) 7.836 → 7.84 (2 d.p.)
(b) 15.097 → 15.10 (2 d.p.)
(c) 0.004382 → 0.00 (2 d.p.)
Explanation: Round to two places after decimal.
4.
397 ≈ 400, 62 ≈ 60
Estimated value = 400 × 60 = 24 000
Explanation: Use 1 significant figure for each number.
5.
892 ≈ 900, 297 ≈ 300
Estimated value = 900 ÷ 300 = 3
Explanation: Round to 1 significant figure to simplify.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
0.000973 = 9.73 × 10⁻⁴
(a) 1 s.f. → 0.0009
(b) 2 s.f. → 0.00097
(c) 3 s.f. → 0.000973
Explanation: Shift until first non-zero digit appears, then round.
7.
12.486 cm
(a) 12.5 cm (1 d.p.)
(b) 12.49 cm (2 d.p.)
(c) 12.5 cm (3 s.f.)
Explanation: Decimal place rounds after decimal; significant figures start from the first non-zero.
8.
498 ≈ 500, 0.052 ≈ 0.05
Estimated value = 500 ÷ 0.05 = 10 000
Explanation: Division becomes easy with 1 significant figure approximation.
9.
√38 ≈ √40 ≈ 6 (to 1 s.f.), 0.412 ≈ 0.4
Estimated value = 6 × 0.4 = 2.4
Explanation: Approximate square root and decimal to 1 s.f.
10.
(a) 3.49 → 3
(b) 8.51 → 9
(c) 12.5 → 13
Explanation: Round to nearest whole number.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
8 496 325
(a) ≈ 8 000 000 (nearest million)
(b) ≈ 8 500 000 (nearest hundred thousand)
(c) ≈ 8 500 000 (2 s.f.)
Explanation: Look at digit after required place for rounding.
12.
47 ≈ 50, 191 ≈ 200
Estimated value = 50 × 200 = 10 000
Explanation: Use 1 significant figure approximations.
13.
0.0007648
(a) 1 s.f. → 0.0008
(b) 2 s.f. → 0.00076
Explanation: Keep required number of digits, round next digit.
14.
628 ≈ 600, 51 ≈ 50, 302 ≈ 300
Estimated value = 600 × 50 ÷ 300 = 30 000 ÷ 300 = 100
Explanation: Approximate each to 1 s.f. before calculating.
15.
(a) 0.009382 → 0.0094 (2 s.f.)
(b) 78541 → 79 000 (2 s.f.)
(c) 63.287 → 63 (2 s.f.)
Explanation: Keep two significant digits only.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course