Interpreting precision and reasonable answers | Year 9

01 / LEARN

The idea, step by step

Round once, at the end

Rounding an intermediate value changes the next calculation. Keep pi, square roots and calculator values unrounded while using them. Then round the final answer to the requested decimal places or sensible measurement precision. An exact expression can be more informative than a long decimal.

36 π \approx 113.097 \dots

, so to one decimal place use

113.1

Ask whether the size makes sense

A correct formula can still give a wrong-looking answer if units were mixed. Estimate the scale before calculating: a tank several metres across should hold thousands of litres, not a few litres. Check whether you were asked for length, area or volume. More decimal places do not make an imprecise measurement more trustworthy; a result should not pretend to be more exact than the information warrants.

A common trap

Reporting every calculator digit or rounding each stage to one decimal place.

Instead: Carry precision through the method, then round the final quantity to the requested accuracy and include its unit.

02 / WORKED EXAMPLES

See the thinking

Example 1

Avoid rounding pi early

A closed cylinder has radius 2 cm and height 7 cm. Find its surface area to one decimal place.

$A = 2 π (2^{2}) + 2 π (2) (7) = 36 π$ cm².
$36 π \approx 113.097$ cm², so the answer is 113.1 cm².
Using $π \approx 3.1$ early would give 111.6 cm², an unnecessary loss of accuracy.

113.1 cm²

Example 2

Check a capacity claim

A tank has internal dimensions 3 m by 2 m by 1.25 m. A student says its capacity is 7.5 L. Explain and correct the answer.

The volume calculation $3 \times 2 \times 1.25 = 7.5$ is in cubic metres.
$1$ m³ holds $1000$ L, so $7.5$ m³ holds $7500$ L.
A tank this size could not hold only a few drink bottles.

7500 L; the student confused cubic metres with litres.

Check your understanding

Round $10 \sqrt{2}$ cm to one decimal place.

Show answer

14.1 cm.

Use the full value $14.142 \dots$ before rounding.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

A cylinder has radius 4 cm and height 5 cm. Give its volume to one decimal place.
2 marks
A calculated length is $\sqrt{50}$ m. Round it to two decimal places.
2 marks
A square has a stated side length of 2.35 m. Calculate its perimeter.
2 marks
A rectangular plot is 6.8 m by 4.2 m. Give its area to one decimal place.
2 marks
A height is recorded as 1.20 m to the nearest 0.01 m. State the maximum rounding error in metres.
2 marks
A student uses $\sqrt{2} \approx 1.4$ to calculate $10 \sqrt{2}$ and reports 14.0 cm. Find the correct answer to one decimal place and explain the difference.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A cylinder has radius 4 cm and height 5 cm. Give its volume to one decimal place.
2 marks
$V = π (4^{2}) (5) = 80 π \approx 251.327$ cm³, giving 251.3 cm³.
251.3 cm³
A calculated length is $\sqrt{50}$ m. Round it to two decimal places.
2 marks
$\sqrt{50} = 7.071067 \dots$ , so the answer is 7.07 m.
7.07 m
A square has a stated side length of 2.35 m. Calculate its perimeter.
2 marks
$P = 4 (2.35) = 9.40$ m, written as 9.4 m.
9.4 m
A rectangular plot is 6.8 m by 4.2 m. Give its area to one decimal place.
2 marks
$6.8 \times 4.2 = 28.56$ m², which rounds to 28.6 m².
28.6 m²
A height is recorded as 1.20 m to the nearest 0.01 m. State the maximum rounding error in metres.
2 marks
The recording step is 0.01 m. Its half-step is 0.005 m.
0.005 m
A student uses $\sqrt{2} \approx 1.4$ to calculate $10 \sqrt{2}$ and reports 14.0 cm. Find the correct answer to one decimal place and explain the difference.
3 marks
$10 \sqrt{2} = 14.142 \dots$ cm. Rounding only at the end gives 14.1 cm.
14.1 cm; the square root was rounded too early.

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Curriculum reference & lesson scope

Australian Curriculum v9 / South Australian Curriculum

Year 9 surface area and volume of right prisms and cylinders, capacity, absolute/relative/percentage measurement error, precision and practical measurement problems.

Official curriculum source ↗

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