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NumberFoundation and Higher

Estimation GCSE questions with answers

6 estimation questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

Estimation questions ask you to round every number to 1 significant figure, then work out the calculation by hand. Write the rounded numbers down, as they show that you estimated rather than guessed.

Quiz yourself: 6 questions

Worked example 1: estimate by rounding to 1 significant figure

Work out an estimate for 3.84 × 4.26. Round each number to 1 significant figure.

  1. Round each number to 1 significant figure: 3.84 ≈ 4, 4.26 ≈ 4.
  2. 4 × 4 = 16.
  3. So an estimate is 16.

Answer 16

01 / Quiz yourselfTry it, then tap to check

Estimation questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Estimate by rounding to 1 significant figureBoth tiers

Work out an estimate for 9.37 × 336. Round each number to 1 significant figure.

Show the answer and working
  1. Round each number to 1 significant figure: 9.37 ≈ 9, 336 ≈ 300.
  2. 9 × 300 = 2,700.
  3. So an estimate is 2,700.

Answer 2,700

02 / Estimate by rounding to 1 significant figureBoth tiers

Work out an estimate for 237 + 3817.74. Round each number to 1 significant figure.

Show the answer and working
  1. Round each number to 1 significant figure: 237 ≈ 200, 381 ≈ 400, 7.74 ≈ 8.
  2. Top: 200 + 400 = 600.
  3. Then divide: 600 ÷ 8 = 75.
  4. So an estimate is 75.

Answer 75

03 / Estimate by rounding to 1 significant figureBoth tiers

Work out an estimate for 47.5 × 88.98.35. Round each number to 1 significant figure.

Show the answer and working
  1. Round each number to 1 significant figure: 47.5 ≈ 50, 88.9 ≈ 90, 8.35 ≈ 8.
  2. Top: 50 × 90 = 4,500.
  3. Then divide: 4,500 ÷ 8 = 562.5.
  4. So an estimate is 562.5.

Answer 562.5

04 / Estimate by rounding to 1 significant figureBoth tiers

Work out an estimate for 47.7 × 66.4. Round each number to 1 significant figure.

Show the answer and working
  1. Round each number to 1 significant figure: 47.7 ≈ 50, 66.4 ≈ 70.
  2. 50 × 70 = 3,500.
  3. So an estimate is 3,500.

Answer 3,500

05 / Estimate by rounding to 1 significant figureBoth tiers

Work out an estimate for 70.6 × 378. Round each number to 1 significant figure.

Show the answer and working
  1. Round each number to 1 significant figure: 70.6 ≈ 70, 378 ≈ 400.
  2. 70 × 400 = 28,000.
  3. So an estimate is 28,000.

Answer 28,000

06 / Estimate by rounding to 1 significant figureBoth tiers

Work out an estimate for 64.1 × 3.2227.1. Round each number to 1 significant figure.

Show the answer and working
  1. Round each number to 1 significant figure: 64.1 ≈ 60, 3.22 ≈ 3, 27.1 ≈ 30.
  2. Top: 60 × 3 = 180.
  3. Then divide: 180 ÷ 30 = 6.
  4. So an estimate is 6.

Answer 6

02 / What's covered1 kind of question

Estimation at GCSE and where marks go

  • Estimate by rounding to 1 significant figureBoth tiers

Worked example 2: estimate by rounding to 1 significant figure

Work out an estimate for 9.32 × 2.731.75. Round each number to 1 significant figure.

  1. Round each number to 1 significant figure: 9.32 ≈ 9, 2.73 ≈ 3, 1.75 ≈ 2.
  2. Top: 9 × 3 = 27.
  3. Then divide: 27 ÷ 2 = 13.5.
  4. So an estimate is 13.5.

Answer 13.5

A common mistake

Rounding to the nearest whole number instead of 1 significant figure. 0.623 to 1 significant figure is 0.6, not 1, so (93.2 + 94.2) ÷ 0.623 is about (90 + 90) ÷ 0.6 = 300.

03 / Practise itiPhone and iPad

More estimation questions in Show Working

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More number topics

FractionsRoundingStandard formFactors and multiplesNegative numbersCalculating with decimalsFractions, decimals and percentagesPowers and rootsSurdsError intervals and boundsListing and countingOrder of operationsAll GCSE maths topics
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