Accuracy and precision | Year 11

01 / LEARN

The idea, step by step

Understand the idea

Resolution is the smallest marked or displayed change. Accuracy concerns closeness to a reference; repeatability concerns agreement between repeated readings. Repeatedly obtaining the same wrong value can be repeatable but inaccurate.

A rounded value represents an interval. To round to the nearest stated unit, values from half a unit below up to half a unit above give the recorded result; the upper endpoint is excluded under the usual convention.

Choose and apply a method

For 8.4 cm to the nearest 0.1 cm, write $8.35 \leq L < 8.45$ cm. For positive dimensions the smallest possible product uses both lower bounds. A rounding interval is not automatically the full instrument uncertainty.

Absolute error has the measurement unit. Percentage error compares it with a nonzero reference value. State that reference and avoid adding digits that rough measurements do not support.

percentage error = \frac{∣ measured - reference ∣}{∣ reference ∣} \times 100 %

A common trap

Assuming consistent readings must be accurate.

Instead: A systematic offset can make all readings consistent but wrong.

02 / WORKED EXAMPLES

See the thinking

Example 1

Find an interval

A parcel mass is 2.36 kg to the nearest 0.01 kg. State its interval.

Half of 0.01 kg is 0.005 kg.
Subtract and add 0.005; exclude the upper endpoint.

2.355 \leq m < 2.365

kg.

Example 2

Compare with a reference

A scale reads 502 g for a verified 500 g mass. Find absolute and percentage error.

Absolute error is $∣ 502 - 500 ∣ = 2$ g.
Percentage error is $2 / 500 \times 100 = 0.4 %$ .

2 g; 0.4%.

Check your understanding

A length is 43 cm to the nearest centimetre. Give its interval.

Show answer

$42.5 \leq L < 43.5$ cm.

The half-unit margin is 0.5 cm.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Write the interval for 7.2 m to the nearest 0.1 m.
2 marks
Write the interval for 340 g to the nearest 10 g.
2 marks
A thermometer reads 21.4 degrees Celsius when a reference is 20.0 degrees Celsius. Find absolute error.
2 marks
A measured length is 98 cm and its reference is 100 cm. Find percentage error.
2 marks
A scale repeatedly reads 1.05 kg for a verified 1.00 kg mass. Describe its readings.
2 marks
A rectangle is recorded as 4.0 cm by 3.0 cm, each to the nearest 0.1 cm. Find minimum possible area.
3 marks

Read the worked solutions

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

Write the interval for 7.2 m to the nearest 0.1 m.
2 marks
Half a rounding unit is 0.05 m.
$7.15 \leq L < 7.25$ m.
Write the interval for 340 g to the nearest 10 g.
2 marks
Half a 10 g unit is 5 g.
$335 \leq m < 345$ g.
A thermometer reads 21.4 degrees Celsius when a reference is 20.0 degrees Celsius. Find absolute error.
2 marks
$∣ 21.4 - 20.0 ∣ = 1.4$ . No Celsius percentage error is required.
1.4 degrees Celsius.
A measured length is 98 cm and its reference is 100 cm. Find percentage error.
2 marks
$∣ 98 - 100 ∣ / 100 \times 100 = 2 %$ .
2%.
A scale repeatedly reads 1.05 kg for a verified 1.00 kg mass. Describe its readings.
2 marks
The readings agree with one another, not with the reference.
Repeatable but inaccurate by 0.05 kg.
A rectangle is recorded as 4.0 cm by 3.0 cm, each to the nearest 0.1 cm. Find minimum possible area.
3 marks
Lower dimensions are 3.95 cm and 2.95 cm.
$3.95 \times 2.95 = 11.6525$ cm $2$ .
11.6525 cm $2$ .

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

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