Rukasha Maths

GCSE maths Beta

Rounding, estimation and error intervals · Revision guide

Foundation · Number · 1 page in the PDF

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Learning objectives

  • Round to a stated accuracy and estimate calculations.
  • Find the error interval for a rounded positive measurement.

Key ideas

Decimal places count from the decimal point; significant figures start at the first non-zero digit.

Inspect the next digit: five or more rounds up; otherwise keep the selected digit.

Estimate by rounding inputs to convenient numbers; keep full accuracy in exact working.

For usual rounding of positive measurements, use half the rounding step on each side.

v−s2≤x<v+s2(step s, stated value v)v-\frac{s}{2}\le x<v+\frac{s}{2}\quad\text{(step }s\text{, stated value }v\text{)}

The lower boundary is included; the upper boundary is excluded.

Worked examples

Example 1

Find the interval for a length stated to the nearest tenth of a centimetre.

v=7.4,s=0.1,s2=0.05v=7.4,\quad s=0.1,\quad\frac{s}{2}=0.05
7.4−0.05=7.35,7.4+0.05=7.457.4-0.05=7.35,\qquad7.4+0.05=7.45
7.35 cm≤L<7.45 cm7.35\text{ cm}\le L<7.45\text{ cm}

Example 2

Round the decimal to two significant figures.

The next digit is eight, so round up.

0.04786≈0.048(2 significant figures)0.04786\approx0.048\quad\text{(2 significant figures)}
0.0480.048

Watch out

Leading zeros are not significant figures. Do not round intermediate steps unless the question requests an estimate.