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GCSE Maths · Number

Rounding GCSE Questions and Worked Answers

Rounding replaces a number with the nearest value at a stated level of precision. Keep its size, use the next digit to choose the nearer value, and round only once.

Foundation & Higher6 worked examples10 original questions
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Start with the meaning

What you need to know about rounding

A length of 6.48 cm sits between the whole-centimetre marks 6 and 7. It is closer to 6, so to the nearest centimetre we report 6 cm. We have deliberately lost some detail, not changed the actual length. This is rounding.

See the idea first

First choose which place you are keeping

Decimal places count digits after the decimal point. Significant figures count from the first non-zero digit, wherever that digit is. A zero after that starting point can still be significant.

The same number at different precisions
NumberInstructionResult
0.047362 decimal places0.05
0.047362 significant figures0.047
6.481 decimal place6.5
6.48nearest whole number6
From problem to method

Typical problems you need to be able to solve

These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.

Round a measurement

What the problem asks: Round 3.746 m to two decimal places.

How to solve it: Keep the hundredths digit, 4. The next digit is 6, so round up to 3.75 m.

Round a small number

What the problem asks: Round 0.00682 to two significant figures.

How to solve it: Start counting at 6. Keep 6 and 8; the following 2 does not round them up. The result is 0.0068.

Choose a practical whole number

What the problem asks: How many 8-seat vans are needed for 35 passengers?

How to solve it: 35 ÷ 8 = 4.375. Four vans are insufficient, so use five. This is rounding up to meet a constraint, not rounding to the nearest integer.

A reliable routine

Round to a stated precision

This method applies when asked for the nearest whole number, decimal place or significant figure. The halfway point determines which neighbouring value is closer; in ordinary GCSE positive-number questions, a tie rounds up.

  1. Locate the last place to keep.
  2. Look at the very next digit: 0–4 keeps the retained digit; 5–9 increases it.
  3. Remove later decimal digits or replace later whole-number digits with zeros.
  4. Keep any trailing zero needed to show the requested decimal precision.

Check: Work from the original value. Rounding in two stages can change the final answer.

Fully worked

Rounding GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Nearest hundred

1 mark
Question

Round 37,651 to the nearest hundred.

Keep the hundreds digit 6. The tens digit is 5, so increase 6 to 7 and replace tens and units with zeros.

37651≈3770037651\approx37700

Tip: the answer stays around 38 thousand.

Example 2

Decimal places

1 mark
Question

Round 5.284 to two decimal places.

The hundredths digit is 8 and the next digit is 4. Keep 8:

5.284≈5.285.284\approx5.28
Example 3

Carry across a nine

2 marks
Question

Round 9.997 to two decimal places.

The next digit is 7, so 9.99 increases by 0.01.

9.99+0.01=10.009.99+0.01=10.00

Write 10.00 to show two decimal places.

Example 4

Significant figures

2 marks
Question

Round 0.004786 to three significant figures.

The first significant digit is 4. Keep 4, 7 and 8; the next digit is 6.

0.004786≈0.004790.004786\approx0.00479

Leading zeros locate the number, but do not count.

Example 5

Truncating versus rounding

2 marks
Question

Truncate 8.376 to two decimal places. Separately, round the original 8.376 to two decimal places.

Truncating simply cuts off later digits: 8.37. Rounding uses the next digit, 6: 8.38. These are different instructions.

Example 6

Avoid double rounding

2 marks
Question

Round 2.449 to one decimal place. Explain why first rounding to two decimal places is risky.

From the original number, the hundredths digit is 4, so the answer is 2.4. An intermediate 2.45 would then round to 2.5. Tip: keep the original display until the requested final rounding.

10 original questions · total 12 marks

Rounding GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 17 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
1

Nearest ten

1 mark

Round 583 to the nearest ten.

Show worked answer

The units digit is 3, so keep the tens digit: 580.

2

Nearest thousand

1 mark

Round 84,620 to the nearest thousand.

Show worked answer

The hundreds digit is 6, so round 84 thousand up to 85,000.

3

One decimal place

1 mark

Round 12.76 to one decimal place.

Show worked answer

The hundredths digit 6 rounds the tenths digit up: 12.8.

4

A necessary zero

1 mark

Round 4.203 to two decimal places.

Show worked answer

The third decimal digit is 3, so the result is 4.20. The final zero records the requested precision.

5

Small value

1 mark

Round 0.00864 to two significant figures.

Show worked answer

Start with 8, then 6. The next digit 4 does not round up, so 0.0086.

6

Large value

1 mark

Round 752,300 to two significant figures.

Show worked answer

Keep 7 and 5. The next digit is 2: 750,000.

7

Across a place boundary

1 mark

Round 0.0997 to two significant figures.

Show worked answer

Keep the two 9s and use the following 7. Rounding carries to 0.10; the zero is the second significant figure.

8

Truncation

1 mark

Truncate 17.986 to one decimal place.

Show worked answer

Keep one digit after the decimal point without rounding: 17.9.

9

Enough packs

2 marks

Pencils are sold in packs of 12. Find the minimum packs needed for 67 pupils to receive one each.

Show worked answer
67÷12=5.5833…67\div12=5.5833\ldots

Five packs contain only 60 pencils; six contain 72. Buy 6 packs.

10

Calculate then round

2 marks

Calculate 17 ÷ 6, giving the answer to two decimal places.

Show worked answer
17÷6=2.8333…17\div6=2.8333\ldots

The third decimal digit is 3, so the answer is 2.83.

Examiner-style feedback

Common rounding mistakes

Counting leading zeros

In 0.0037, the first significant figure is 3, not a zero.

Dropping place value

Rounding 6,830 to one significant figure gives 7,000, not 7.

Always rounding to nearest

People, packs and capacity may require a whole number above or below the quotient. Read the practical constraint.

30-second recap

Choose, carry out, check

Translate the wording before you reach for a rule.

  1. Locate the retained place.
  2. Use only the next digit to decide.
  3. Preserve size and required zeros.
  4. Round the original value once.
Quick answers

Rounding FAQ

Is 4.20 the same value as 4.2?

Yes, but 4.20 explicitly shows two decimal places.

Does rounding give an exact answer?

Usually not. Use an approximation sign or state the precision. A rounded measurement represents a range of possible originals.

Build connected skills

What to revise next

Browse all GCSE Maths study guidesReview the worked examplesTry the questions again
Content standards

Curriculum and rights review

N15: positive-number rounding, truncation and contextual integer decisions across tiers. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.

Official specification references