IGCSE Mathematics 0580 · Topic 1.5

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.

Cambridge IGCSE Mathematics (0580) · Topic 1.5: Ordering and Rounding

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

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.

Question 1[3 marks]

Write 0.004683 correct to 2 significant figures, and correct to 3 decimal places.

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Answer: 0.0047 to 2 significant figures, and 0.005 to 3 decimal places.
  1. For significant figures, start counting at the first non-zero digit, which is 4. The second significant figure is 6.
  2. The next digit is 8, which is 5 or more, so round the 6 up to 7. The answer is 0.0047.
  3. For decimal places, count digits after the point: 0 is the first, 0 the second, 4 the third.
  4. The next digit is 6, which is 5 or more, so round the 4 up to 5. The answer is 0.005.
How the marks are awarded. 1 mark for identifying 4 as the first significant figure. 1 mark for 0.0047. 1 mark for 0.005.
Where students lose the mark. Counting the leading zeros as significant figures, giving 0.0046 rounded from the wrong position. Significant figures always start at the first non-zero digit.
Question 2[3 marks]

Write the numbers minus three quarters, minus 0.7 and minus five eighths in order, starting with the smallest.

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Answer: minus three quarters, minus 0.7, minus five eighths.
  1. Convert each to a decimal so they can be compared directly.
  2. minus three quarters = minus 0.75, minus 0.7 is already a decimal, and minus five eighths = minus 0.625.
  3. 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.
  4. In order from smallest: minus three quarters, then minus 0.7, then minus five eighths.
How the marks are awarded. 1 mark for converting all three to decimals. 1 mark for recognising that a larger digit after the minus sign means a smaller value. 1 mark for the correct order.
Where students lose the mark. Ordering the negatives as though they were positive, which reverses the sequence. Minus 0.75 is less than minus 0.625, not greater.
Question 3[3 marks]

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.

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Answer: 200
  1. Round each value to 1 significant figure: 4.87 becomes 5, 19.6 becomes 20, and 0.51 becomes 0.5.
  2. The estimated calculation is 5 multiplied by 20, divided by 0.5.
  3. 5 x 20 = 100, and 100 divided by 0.5 = 200.
  4. The estimate is therefore 200. The true value is about 187, so the estimate is reasonable.
How the marks are awarded. 1 mark for rounding all three values to 1 significant figure and showing them. 1 mark for a correct simplified calculation. 1 mark for 200.
Where students lose the mark. Using a calculator on the original figures and then rounding the answer. Estimation marks are awarded for rounding first and showing the simplified calculation.
Question 4[3 marks]

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.

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Answer: 4.65 is less than or equal to x, which is less than 4.75.
  1. Rounding to 1 decimal place means the true value lies within half of 0.1, which is 0.05, of the recorded value.
  2. The smallest value that rounds to 4.7 is 4.65, because 4.65 rounds up.
  3. The largest values are just below 4.75, because 4.75 would round up to 4.8.
  4. 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.
How the marks are awarded. 1 mark for a lower bound of 4.65. 1 mark for an upper bound of 4.75. 1 mark for using the inclusive symbol on the lower bound and the strict symbol on the upper bound.
Where students lose the mark. Writing the upper bound as 4.749 or using an inclusive symbol on it. Convention places the upper bound at exactly 4.75 with a strict inequality.

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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.

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Related IGCSE Mathematics topics

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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.