Rounding: Decimal Places and Significant Figures –

Rounding is a core skill tested on every GCSE Maths paper. You must be able to round numbers to a given number of decimal places (dp) or significant figures (sf), and know when to round during multi-step calculations.

What Is Rounding?

Rounding means replacing a number with an approximation that is simpler to use while staying close to the original value. The two main types at GCSE are rounding to decimal places and rounding to significant figures.

Decimal places (dp) count the digits after the decimal point. Rounding to 2 dp means keeping two digits after the point.

Significant figures (sf) count from the first non-zero digit. Leading zeros are not significant. For example, in 0.00407, the first significant figure is 4, the second is 0, and the third is 7.

Truncation simply cuts off digits without rounding — the examiners sometimes ask you to distinguish between rounding and truncation.

Key Formulas

Step-by-Step Method

1. Identify whether you are rounding to decimal places or significant figures.
2. Count to the required position and look at the next digit (the "deciding digit").
3. If the deciding digit is 5, 6, 7, 8, or 9, increase the last kept digit by 1.
4. If the deciding digit is 0, 1, 2, 3, or 4, keep the last digit unchanged.
5. For significant figures, replace remaining digits with zeros if they come before the decimal point.

Worked Example 1 — Foundation Level

Question: Round 3.4562 to 2 decimal places.

Working:

Step 1 — The second decimal place is 5 (3.4562).

Step 2 — The deciding digit (third decimal place) is 6. Since 6 ≥ 5, round up.

Step 3 — The 5 becomes 6.

Answer: 3.46

Worked Example 2 — Higher Level

Question: Round 0.004073 to 2 significant figures.

Working:

Step 1 — The leading zeros are not significant. The first significant figure is 4, the second is 0 (0.004073).

Step 2 — The deciding digit (third sf) is 7. Since 7 ≥ 5, round up.

Step 3 — The 0 becomes 1: 0.0041.

Answer: 0.0041

Worked Example 3 — Exam Style

Question: A calculator shows 7.9985. Round this to 3 significant figures.

Working:

Step 1 — The first three significant figures are 7, 9, 9 (7.99|85).

Step 2 — The deciding digit is 8. Since 8 ≥ 5, round up.

Step 3 — 7.99 rounds up: 9 becomes 10, which carries over. 7.99 becomes 8.00.

Answer: 8.00

Common Mistakes

• Confusing decimal places with significant figures. In 0.0035, rounding to 2 dp gives 0.00, but rounding to 2 sf gives 0.0035.
• Forgetting trailing zeros matter. 3.50 to 2 dp is different from 3.5 — the zero shows you have rounded to 2 decimal places. Always include trailing zeros when required.
• Rounding too early in multi-step problems. Keep full precision during working and only round your final answer. Premature rounding can lead to inaccurate results.

Exam Tips

• Read the question carefully to see whether it asks for decimal places or significant figures.
• When the question says "give your answer to a suitable degree of accuracy", 3 significant figures is usually appropriate.
• For estimation questions, round each value to 1 significant figure before calculating.

Practice Questions

Q1 (Foundation): Round 47,356 to 3 significant figures.

Q2 (Foundation): Round 0.08247 to 2 decimal places.

Q3 (Higher): A number is truncated to 1 decimal place to give 4.7. Write down the error interval for the original number.

Practise rounding questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Bounds and Error Intervals
• Decimals
• Estimating Square Roots

Summary

• Decimal places count digits after the decimal point.
• Significant figures count from the first non-zero digit.
• Look at the deciding digit: 5 or more rounds up, less than 5 rounds down.
• Truncation cuts digits off without rounding — know the difference.
• Avoid rounding intermediate steps; only round the final answer.