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N14, N15Rounding, estimation and error intervals

Edexcel GCSE Maths (1MA1), Higher tier · Number

Practise Rounding, estimation and error intervals. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy3 marks
(a) Round \(22{,}201\) to 2 significant figures.[1]
(b) Round \(94{,}256.5\) to the nearest 10.[1]
(c) Round \(54.95\) to 1 decimal place.[1]
Show the answer and mark scheme
(a) Answer: \(22{,}000\)
  • B1 for 22,000

Worked solution: \(22{,}201 \approx 22{,}000\) (2 s.f.)

(b) Answer: \(94{,}260\)
  • B1 for 94,260

Worked solution: \(94{,}256.5 \approx 94{,}260\)

(c) Answer: \(55.0\)
  • B1 for 55.0 cao

Worked solution: Look at the second decimal place: \(54.95 \approx 55.0\)

Question 2Medium4 marks
Nia wants an estimate for the value of \(\frac{38.7 \times 0.493}{0.0213}\).
(a) By rounding each number to 1 significant figure, work out an estimate for the value.[2]
(b) Without working out the exact value, explain whether your estimate is an overestimate or an underestimate.[2]
Show the answer and mark scheme
(a) Answer: 1000
  • M1 for \(\frac{40 \times 0.5}{0.02}\) (all three numbers correctly rounded)
  • A1 for 1000

Worked solution: \(\frac{40 \times 0.5}{0.02} = \frac{20}{0.02} = 1000\)

(b) Answer: Overestimate: 38.7 and 0.493 were both rounded up, so the numerator is too big, and 0.0213 was rounded down, and dividing by a smaller number gives a bigger answer.
  • C1 for stating that 38.7 and 0.493 were both rounded up, so the top of the fraction is too large
  • C1 for stating that 0.0213 was rounded down, so dividing by the smaller number makes the answer larger, with the conclusion 'overestimate'

Worked solution: 40 > 38.7 and 0.5 > 0.493, so the numerator is larger than it should be.
0.02 < 0.0213, and dividing by a smaller number gives a larger result.
Every change makes the value larger, so 1000 is an overestimate (the actual value is about 896).

Question 3Hard3 marks
Work out an estimate for the value of \(\frac{(2.77 \times 10^{5}) \times (8.27 \times 10^{-4})}{2.08 \times 10^{-3}}\)
Give your answer in standard form.
You must show your working.[3]
Show the answer and mark scheme
Answer: \(1.2 \times 10^{5}\)
  • M1 for rounding all three numbers to 1 significant figure, e.g. \(3 \times 10^{5},\ 8 \times 10^{-4},\ 2 \times 10^{-3}\)
  • M1 for \(3 \times 8 \div 2 = 12\) or \(10^{5} \times 10^{-4} \div 10^{-3} = 10^{4}\)
  • A1 for \(1.2 \times 10^{5}\) cao

Worked solution: Round each number to 1 significant figure: \(\frac{3 \times 10^{5} \times 8 \times 10^{-4}}{2 \times 10^{-3}} = \frac{24}{2} \times 10^{5 + (-4) - (-3)} = 12 \times 10^{4} = 1.2 \times 10^{5}\)

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