IGCSE Mathematics: Ordering and Rounding Practice Questions
Rounding to significant figures counts from the first non-zero digit, while rounding to decimal places counts from the decimal point. Estimation means rounding every value to one significant figure before calculating.
Topic 1.5 of Cambridge IGCSE Mathematics 0580 affects every other topic, because most answers must be given to three significant figures. Leading zeros are where students lose marks, since they never count as significant. The questions below cover rounding, ordering and estimation.
What you need to know for Ordering and Rounding
- Significant figuresCount from the first non-zero digit. In 0.004683 the first significant figure is the 4. Zeros before it are placeholders and are not significant.
- Decimal placesCount digits after the decimal point, including any zeros. 0.004683 to 3 decimal places is 0.005.
- Rounding ruleLook at the digit after the one you are keeping. If it is 5 or more, round up. If it is 4 or less, round down.
- Ordering negative numbersThe further a negative number is from zero, the smaller it is. So minus 0.75 is less than minus 0.7.
- EstimationRound every number in the calculation to one significant figure, then work out the simplified calculation. Show the rounded values, because that is where the method mark sits.
- Inequality notationA value x rounded to 1 decimal place as 4.7 satisfies 4.65 is less than or equal to x, which is less than 4.75.
IGCSE Mathematics Ordering and Rounding questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
Write 0.004683 correct to 2 significant figures, and correct to 3 decimal places.
Show the worked answer
- For significant figures, start counting at the first non-zero digit, which is 4. The second significant figure is 6.
- The next digit is 8, which is 5 or more, so round the 6 up to 7. The answer is 0.0047.
- For decimal places, count digits after the point: 0 is the first, 0 the second, 4 the third.
- The next digit is 6, which is 5 or more, so round the 4 up to 5. The answer is 0.005.
Write the numbers minus three quarters, minus 0.7 and minus five eighths in order, starting with the smallest.
Show the worked answer
- Convert each to a decimal so they can be compared directly.
- minus three quarters = minus 0.75, minus 0.7 is already a decimal, and minus five eighths = minus 0.625.
- For negative numbers, the further from zero the smaller the value. So minus 0.75 is the smallest and minus 0.625 is the largest.
- In order from smallest: minus three quarters, then minus 0.7, then minus five eighths.
By rounding each number to 1 significant figure, estimate the value of 4.87 multiplied by 19.6, all divided by 0.51. Show the rounded values you use.
Show the worked answer
- Round each value to 1 significant figure: 4.87 becomes 5, 19.6 becomes 20, and 0.51 becomes 0.5.
- The estimated calculation is 5 multiplied by 20, divided by 0.5.
- 5 x 20 = 100, and 100 divided by 0.5 = 200.
- The estimate is therefore 200. The true value is about 187, so the estimate is reasonable.
A length x, measured to 1 decimal place, is recorded as 4.7 cm. Write down an inequality showing the range of possible values of x.
Show the worked answer
- Rounding to 1 decimal place means the true value lies within half of 0.1, which is 0.05, of the recorded value.
- The smallest value that rounds to 4.7 is 4.65, because 4.65 rounds up.
- The largest values are just below 4.75, because 4.75 would round up to 4.8.
- So 4.65 is less than or equal to x, and x is less than 4.75. The lower bound uses the inclusive symbol and the upper bound the strict one.
Common mistakes in this topic
- Counting leading zeros as significant figures.
- Confusing significant figures with decimal places.
- Ordering negative numbers as though they were positive.
- Estimating with a calculator instead of rounding first.
- Rounding partway through a multi step calculation instead of at the end.
Exam tips
- Underline the digit you are rounding to, then look at the one immediately after it. That habit removes most errors.
- In estimation questions, always write out the rounded calculation. It carries a mark whatever the final answer.
- Keep full accuracy in your calculator throughout a long calculation and round only the final answer.
- For ordering, convert everything to decimals first. Mixed formats are where errors creep in.
- Unless told otherwise, give final answers to 3 significant figures. Cambridge states this on the front of the paper.
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Ordering and Rounding FAQs
What is the difference between significant figures and decimal places?
Significant figures are counted from the first non-zero digit, so leading zeros never count. Decimal places are counted from the decimal point and do include zeros. The number 0.004683 is 0.0047 to 2 significant figures but 0.005 to 3 decimal places.
How do I estimate an answer?
Round every number in the calculation to one significant figure, then perform the simplified calculation. Show the rounded values in your working, because the method mark is awarded for rounding first rather than for the final figure.
How do I order negative numbers?
Convert everything to decimals first, then remember that the further a negative number sits from zero, the smaller it is. So minus 0.75 is smaller than minus 0.7, which is smaller than minus 0.625. Ordering them as though they were positive reverses the sequence.
To how many figures should I give my answers?
Cambridge asks for answers correct to three significant figures unless the question specifies otherwise, with angles given to one decimal place. Keep full accuracy on your calculator throughout and round only at the very end.
Continue through the IGCSE Mathematics syllabus
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.