Estimation and Checking
Estimation means finding an approximate answer to a calculation, usually by rounding every number in it to 1 significant figure first, so the size of the true answer can be judged quickly and without a calculator. Checking means testing whether a calculated answer is correct or sensible, using an estimate, the inverse operation, or the context of the question, catching mistakes such as a misplaced decimal point before an answer is written down as final.
Before you start
Make sure you're comfortable with these topics first:
Method
- To estimate a calculation, round every number in it to 1 significant figure first.
- Work out the rounded calculation using numbers that are easy to calculate mentally.
- State the estimate clearly, and use it to judge whether a calculator answer has the right order of magnitude.
- To check an addition or subtraction, use the inverse operation on your answer to see if it returns the original numbers.
- To check a multiplication or division, use the inverse operation, or check that the answer's size makes sense (for example, dividing by a number greater than 1 should give a smaller answer).
- Always check that an answer makes sense in the context of the question, such as a length not being negative or a number of people not being a decimal.
Worked example
Jess buys 18 tickets at 4.85 pounds each. Estimate the total cost by rounding each number to 1 significant figure, then use a written method to find the exact total cost, and check your exact answer against the estimate.
- Round 18 to 1 significant figure: 20. Round 4.85 to 1 significant figure: 5.
- Estimate: 20 x 5 = 100 pounds.
- Work out the exact total: 18 x 4.85. First find 18 x 5 = 90, then subtract 18 x 0.15 = 2.70, giving 90 - 2.70 = 87.30.
- Check by multiplying a different way: 4.85 x 18 = 4.85 x 10 + 4.85 x 8 = 48.50 + 38.80 = 87.30. This matches, confirming the exact total is 87.30 pounds.
- Compare with the estimate: 87.30 is reasonably close to the estimate of 100, so the exact answer has the right order of magnitude and is likely correct.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Estimate the value of 289 x 41 by rounding each number to 1 significant figure.Show answer
Answer: 12000 (300 x 40)
Q2Estimate the value of 7,920 / 38 by rounding each number to 1 significant figure.Show answer
Answer: 200 (8000 / 40)
Q3By rounding to 1 significant figure, 48 x 0.19 can be estimated as approximately 10. Use this estimate to decide whether a calculator answer of 91.2 is correct. Explain your answer.Show answer
Answer: No, 91.2 is not correct; since the estimate is about 10, the exact answer should be close to 10, so the decimal point in 91.2 must be misplaced (the correct value is 9.12).
Q4Use the inverse operation to check whether 6.3 + 4.8 = 11.1 is correct.Show answer
Answer: Correct; 11.1 - 4.8 = 6.3, which matches the first number, so the addition is correct.
Q5A shop assistant calculates that 7 items costing 3.20 pounds each come to 224 pounds in total. Use an estimate to show this answer must be wrong.Show answer
Answer: Estimate: 7 x 3 = 21 pounds, so the true total should be about 21 pounds, not 224 pounds (the correct total is 22.40 pounds); the assistant has made an error, most likely a misplaced decimal point.
Q6Tom says 5,304 / 4 = 1,326. Check whether Tom is correct using the inverse operation.Show answer
Answer: Correct; 1,326 x 4 = 5,304, which matches, so Tom's division is correct.
Q7Without a calculator, decide whether 61 x 0.9 is bigger or smaller than 61. Explain your reasoning.Show answer
Answer: Smaller; multiplying by a number less than 1 makes the result smaller than the original number, so 61 x 0.9 = 54.9, which is less than 61.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
By rounding each number to 1 significant figure, estimate the value of (798 x 3.1) / 39. Show your rounded values.
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A landscaper calculates that 6 paving slabs, each costing 24.50 pounds, will cost 147.00 pounds in total. (a) Use estimation, rounding each number to 1 significant figure, to check whether this total is reasonable. (b) State, with a reason, whether the landscaper's answer is likely to be correct.
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A student calculates 812 / 0.4 and gets an answer of 20.3. (a) Use estimation to show that this answer cannot be correct. (b) Explain, in terms of dividing by a number less than 1, why the correct answer should be bigger than 812.
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Free printable worksheet
Want more practice on paper? Download the estimation and checking worksheet pack - 3 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 14 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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