Rounding and Estimating to Check an Answer
Rounding and estimating to check an answer covers rounding numbers to a stated degree of accuracy, such as the nearest whole number, ten or significant figure, and using rounded values to estimate the size of a calculation before working it out exactly. On a timed 11+ paper this is the key checking skill: a quick estimate shows whether a full answer is roughly the right size, catching mistakes such as a misplaced decimal point.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify which place value you are rounding to, and look at the digit immediately to its right to decide whether to round up or down.
- If that digit is 5 or more, round the target digit up by one; if it is 4 or less, leave the target digit as it is.
- Replace every digit after the rounded place with a zero for a whole number, or remove it for a decimal.
- To estimate a calculation, round each number in it to 1 significant figure, or another convenient value, before calculating, so the working stays quick.
- Use the word 'about' or the phrase 'approximately equal to' when writing an estimate, since it is not the exact answer.
- Compare an exact answer to your estimate: if they are very different in size, a mistake has probably been made somewhere.
Worked example
Estimate the value of 396 x 5.2 by rounding each number to 1 significant figure, then use your estimate to check whether the exact answer, 2059.2, is reasonable.
- Round 396 to 1 significant figure: 400.
- Round 5.2 to 1 significant figure: 5.
- Multiply the rounded values: 400 x 5 = 2000.
- Compare the estimate, 2000, with the exact answer, 2059.2: the two values are close in size.
- Final answer: since 2059.2 is close to the estimate of 2000, it is a reasonable answer.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Round 4832 to the nearest hundred.Show answer
Answer: 4800
Q2Round 17.68 to the nearest whole number.Show answer
Answer: 18
Q3Round 0.0472 to 1 significant figure.Show answer
Answer: 0.05
Q4Estimate 58 x 21 by rounding each number to 1 significant figure.Show answer
Answer: 1200 (60 x 20)
Q5A shop's till shows a bill of 179.40 pounds for 6 identical items. Estimate the price of one item by rounding the total to the nearest 10 pounds first.Show answer
Answer: About 30 pounds (180 divided by 6 = 30)
Q6True or False: an estimate should use the exact same numbers as the real calculation.Show answer
Answer: False (an estimate uses rounded numbers to make the working faster)
Q7Explain why estimating before doing a calculation is a useful check, even when you plan to use a calculator.Show answer
Answer: An estimate gives a rough idea of the size the answer should be, so if the exact calculated answer is very different from the estimate, it signals that a mistake was probably made, such as a wrong button press or a misplaced decimal point.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Round 6.385 to 2 decimal places, showing which digit determines your rounding.
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A school orders 312 chairs to be arranged as evenly as possible across 29 rows. (a) Estimate 312 divided by 29 by rounding each number to 1 significant figure. (b) Given that the exact value of 312 divided by 29, to 2 decimal places, is 10.76, explain whether your estimate in part (a) is reasonable.
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Free printable worksheet
Want more practice on paper? Download the rounding and estimating to check an answer worksheet pack - 7 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 40 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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