N7NumberFoundation

Rounding & Estimation

Rounding makes numbers simpler to use and lets you estimate answers quickly. Knowing decimal places and significant figures — and how to estimate — saves easy marks in every exam.

30 min Video by Maths Genie AQA GCSE Maths

Rounding to Decimal Places and Significant FiguresWatch the walkthrough, then read the notes below.

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What you'll learn

Round to a given number of decimal places
Round to significant figures
Estimate calculations by rounding to 1 s.f.
Understand when an estimate is enough

Decimal places and significant figures

To round, look at the next digit: if it is 5 or more, round up; otherwise round down. $Decimal places$ count digits after the point. $Significant figures$ count from the first non-zero digit.

1The 2nd decimal is 4 (less than 5).

2So round down: keep the 8.

Answer

3.8

Estimating

To estimate, round every number to 1 significant figure and then calculate. The symbol $\approx$ means “approximately equal to”.

\frac{38 \times 21}{9} \approx \frac{40 \times 20}{10} = 80

Round to 1 s.f. then work it out.

Tip — Leading zeros are never significant: in 0.0046 the first significant figure is the 4.

Remember these

\geq 5 \Rightarrow round up

Rounding rule.

\approx

“Approximately equal to” — used for estimates.

Watch out for these

Counting leading zeros as significant figures.

Start counting from the first non-zero digit.

Rounding 4.96 to 1 d.p. as 4.9.

The next digit is 6, so it rounds up to 5.0.

Key takeaways

5 or more rounds up; otherwise round down.
Significant figures start at the first non-zero digit.
Estimate by rounding everything to 1 s.f.

Test yourself

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