Estimation
Estimation is a key number topic at GCSE Maths. This Foundation and Higher worksheet gives you exam-style questions on estimating answers, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. Round each number to 1 significant figure first, then calculate.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
Estimation replaces awkward numbers with easy ones so a calculation can be done mentally. It gives an approximate answer that checks whether an exact calculation is sensible.
The standard technique is rounding each number to one significant figure. So \(38.2 \times 5.7\) becomes \(40 \times 6 = 240\), which is close enough to confirm an exact answer of \(217.74\) is about right.
Examination questions almost always specify one significant figure, and they expect to see the rounded values written down. Marks are awarded for the rounding as well as the final estimate, so showing that step is essential.
Revision notes
Rounding to one significant figure
Round every number in the calculation to its first significant digit, then carry out the arithmetic.
For \(\frac{28.4 \times 9.7}{5.2}\), round to \(\frac{30 \times 10}{5} = 60\). The exact answer is \(52.98\), so the estimate is a reasonable check.
Estimating with roots
For a square root, find the nearest square number.
To estimate \(\sqrt{78}\), note that \(81\) is close, so the answer is a little under \(9\). This is often quicker than any calculator work.
Deciding if an estimate is over or under
If you rounded numbers up, the estimate is likely too large; if you rounded down, too small.
For \(40 \times 6\) from \(38.2 \times 5.7\), both were rounded up, so the estimate of \(240\) exceeds the true value of \(217.74\). Questions sometimes ask you to justify this.
Key points
- Round each number to one significant figure.
- Show the rounded values in your working.
- Use the nearest square number to estimate a root.
- Rounding up gives an overestimate.
- Rounding down gives an underestimate.
- An estimate checks whether an exact answer is sensible.
Worked examples
Example 1
Estimate \(41.3 \times 7.8\).
Working
Example 2
Estimate \(\dfrac{612 \times 3.9}{19.7}\).
Working
Example 3
Estimate \(\sqrt{62}\).
Working
Common mistakes
Rounding to the nearest whole number instead of 1 significant figure.
612 becomes 600, not 612. One significant figure keeps only the first digit.
Not showing the rounded values.
Marks are awarded for the rounding step, so it must appear in the working.
Using the calculator and then rounding the exact answer.
That is not an estimate. Round first, then calculate mentally.
Rounding a number below 1 incorrectly.
0.048 to one significant figure is 0.05, not 0.
Exam tips
- Write the rounded calculation on its own line before evaluating.
- Use numbers that divide easily, even if slightly different from strict rounding.
- For roots, name the nearest square number in your working.
- Say whether your estimate is likely to be an over or underestimate if asked.
Key terms
- Estimate
- An approximate answer found using rounded values.
- Significant figure
- A digit contributing to a number's accuracy, from the first non-zero digit.
- Overestimate
- An approximation larger than the true value.
- Approximation
- A value close to but not exactly the true answer.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.