Sheet № 130 · Foundation + Higher · AQA · Edexcel · OCR
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.
§Key definitions
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.
Question:
Round 3.4562 to 2 decimal places.
Q1 (Foundation):
Round 47,356 to 3 significant figures.
§Formulas to memorise
To round: look at the digit after the last one you are keeping. If it is 5 or more, round up. If it is less than 5, round down.
Significant figures start from the first non-zero digit, counting all digits from that point
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.
Worked example
Round 3.4562 to 2 decimal places.
Working:
⚠ 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.