Round to the nearest 10, 100 or 1000, to decimal places and to significant figures, and use rounding to estimate. It is a Foundation topic, aimed at grade 1. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Rounding is looking one place further than you need and asking whether that next digit is 5 or more. If it is, the digit you are keeping goes up by one; if not, it stays. 7.849 to 1 decimal place looks at the 4, so it stays 7.8. A 9 that rounds up becomes 0 and the extra 1 carries left: 2.96 to 1 d.p. is 3.0.
Significant figures count from the first non-zero digit. In 0.004072 the first significant figure is the 4, so 2 s.f. is 0.0041. Zeros between non-zero digits count; leading zeros after a decimal point do not.
Nearest 10, 100 or 1000 is the same idea on the other side of the decimal point. 649500 to the nearest 1000 looks at the hundreds digit 5, so it rounds to 650000.
Objectives
Round to the nearest 10 and 100.
Use the next digit as the decider.
Round to 1 decimal place and to 2 significant figures.
Key points
Round whole numbers to the nearest 10, 100 or 1000.
Round decimals to a given number of decimal places (d.p.).
Round any number to a given number of significant figures (s.f.), including numbers like 0.004072.
Estimate a calculation by rounding every number to 1 significant figure first.
Worked examples
Example 1
Round 62 to the nearest 10.
2 marks
62 is between 60 and 70.
The ones digit is 2.
2 is less than 5, so round down to 60.
Answer: 60
Common slips
Slip: 62 is between 50 and 60. 62 is past 60, so the lower ten is 60 not 50.
Slip: The ones digit is 6. The decider for the nearest ten is the ones digit, which is 2.
Slip: Round up to 70. A decider of 2 does not round up.
Example 2
Round 3.46 to the nearest whole number.
2 marks
3.46 is between 3 and 4.
The tenths digit is 4.
4 is less than 5, so the whole number is 3.
Answer: 3
Common slips
Slip: 3.46 is between 3.4 and 3.5. Nearest whole number uses the units, not 1 decimal place.
Slip: The hundredths digit decides a whole number. The first decimal digit decides the nearest integer.
Slip: The answer is 3.5. 3.5 is 1 decimal place, not the nearest whole number.
Example 3
A length is 2 750 m. Round it to the nearest hundred metres, then to the nearest thousand metres.
3 marks
Nearest hundred: the tens digit is 5, so 2 800.
Nearest thousand: the hundreds digit of 2 750 is 7.
7 rounds the thousands up, so 3 000.
Answer: 3000
Common slips
Slip: Tens digit 5 rounds down. Halfway rounds up, so 2 750 goes to 2 800 not 2 700.
Slip: Use the already rounded 2 800 to round again. Round the original number each time. Do not round a rounded number.
Slip: The thousands stay at 2 000. A hundreds digit of 7 is enough to round up.
Questions and answers
GCSE Maths rounding questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Round 41 to the nearest 10.
Show answer
Answer: 40
41 is between 40 and 50.
The ones digit is 1, so the answer is 40.
M1 — 41 is between 40 and 50.
A1 — Answer 40
Question 2 Easy2 marks
Round 85 to the nearest 10.
Show answer
Answer: 90
The ones digit is 5, so round up.
85 rounds to 90.
M1 — The ones digit is 5, so round up.
A1 — Answer 90
Question 3 Medium2 marks
Round 648 to the nearest 100.
Show answer
Answer: 600
The tens digit is 4.
648 rounds down to 600.
M1 — The tens digit is 4.
A1 — Answer 600
Question 4 Medium2 marks
Round 1 250 to the nearest hundred.
Show answer
Answer: 1300
The tens digit is 5, so round up.
1 250 rounds to 1 300.
M1 — The tens digit is 5, so round up.
A1 — Answer 1300
Question 5 Hard2 marks
A crowd of 14 650 is reported to the nearest thousand. What figure is used?
Show answer
Answer: 15000
The hundreds digit is 6.
14 650 rounds to 15 000.
M1 — The hundreds digit is 6.
A1 — Answer 15000
Question 6 Hard2 marks
Round 0.96 to 1 decimal place.
Show answer
Answer: 1.0
The hundredths digit is 6, so the tenths round up.
0.96 rounds to 1.0.
M1 — The hundredths digit is 6, so the tenths round up.
A1 — Answer 1.0
Question 7 Exam-style2 marks
A town has 24 480 people. Round this to the nearest hundred, and say whether that rounded figure is exact.
Show answer
Answer: 24500
The tens digit is 8, so the nearest hundred is 24 500.
24 500 is an approximation, not the exact population.
B1 — Answer 24 500
B1 — States that the rounded figure is not exact
Common mistakes
Most lost marks on this topic are one slip.
Rounding down when the decider is 5.
5 is the halfway case, and the usual rule rounds it up.
Looking at the wrong digit, such as the ones when rounding to the nearest hundred.
Look at the digit immediately after the column you are rounding to.
Rounding a number that has already been rounded, instead of the original.
Each instruction uses the original digits.
Spot the slip
36 is between 30 and 40. Which ten is it nearer?
40
30
35
Show the slip
40 The halfway point is 35. 36 is past halfway, so it rounds up to 40.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the rounded numbers down before calculating in an estimate question — that line usually carries a method mark.
If a question says 'give your answer to 1 decimal place', do all the working in full and round only at the very end.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.