Absolute and percentage error

Find the absolute error of a measurement from the precision of an instrument, and calculate percentage error to compare the precision of different instruments.

Worked examples

Finding the absolute error

Straightforward

Problem

A ruler measures to the nearest millimetre. A book is recorded as

185 \text{ mm}

long. Find the absolute error of this measurement.

Calculating percentage error

Moderate

Problem

A thermometer is accurate to the nearest

2^\circ\text{C}

and records a temperature of

30^\circ\text{C}

. Calculate the percentage error.

Comparing the precision of two instruments

Challenging

Problem

A measuring jug (accurate to the nearest

10 \text{ mL}

) records a volume as

200 \text{ mL}

. A graduated cylinder (accurate to the nearest

1 \text{ mL}

) records the same volume as

197 \text{ mL}

. Calculate the percentage error for each instrument and determine which is more precise.

Practise

Q1·Straightforward

A ruler measures to the nearest millimetre. A pencil is recorded as

47 \text{ mm}

long. What is the absolute error of this measurement, in millimetres?

Q2·Straightforward

A kitchen scale measures to the nearest

10 \text{ g}

. A bag of rice shows a reading of

380 \text{ g}

. What is the absolute error of this measurement, in grams?

Q3·Straightforward

A clinical thermometer measures to the nearest

0.5^\circ\text{C}

. A patient's temperature is recorded as

37.5^\circ\text{C}

. What is the absolute error of this reading, in degrees Celsius?

Q4·Straightforward

A stopwatch measures to the nearest

0.01 \text{ s}

. A sprinter's time is recorded as

11.23 \text{ s}

. What is the absolute error of this measurement, in seconds?

Q5·Moderate

A scale is accurate to the nearest

2 \text{ g}

and records a mass of

40 \text{ g}

. Calculate the percentage error.

Q6·Moderate

A ruler is accurate to the nearest centimetre and records a length of

25 \text{ cm}

. Calculate the percentage error.

Q7·Moderate

A thermometer is accurate to the nearest

2^\circ\text{C}

and records a temperature of

20^\circ\text{C}

. Calculate the percentage error.

Q8·Moderate

A stopwatch accurate to the nearest

0.1 \text{ s}

records a time of

4.5 \text{ s}

. Calculate the percentage error. Give your answer to 2 decimal places.

Q9·Challenging

A tape measure accurate to the nearest centimetre records a board as

60 \text{ cm}

long. A steel rule accurate to the nearest millimetre records the same board as

598 \text{ mm}

. Calculate the percentage error for the tape measure. Give your answer to 2 decimal places.

Q10·Challenging

A digital scale accurate to the nearest

0.5 \text{ g}

records a mass of

125 \text{ g}

. A laboratory balance accurate to the nearest

0.001 \text{ g}

records the same mass as

124.936 \text{ g}

. Calculate the percentage error for the digital scale.

Q11·Challenging

Two thermometers measure the same room temperature. Thermometer A (accurate to the nearest

1^\circ\text{C}

) records

24^\circ\text{C}

. Thermometer B (accurate to the nearest

0.1^\circ\text{C}

) records

24.0^\circ\text{C}

. Which thermometer is more precise?

Thermometer A, because it uses whole numbersThermometer B, because it has a smaller absolute error and a smaller percentage errorBoth are equally precise, because they record the same temperatureThermometer A, because a larger absolute error indicates a wider range of possible values

Q12·Challenging

A steel rod is measured by two instruments. Instrument P (accurate to the nearest

1 \text{ mm}

) records

500 \text{ mm}

. Instrument Q (accurate to the nearest

10 \text{ mm}

) records

500 \text{ mm}

. Which statement correctly describes the comparison?

Instrument Q is more precise because a larger unit of measurement reduces human errorBoth instruments have the same percentage error because they recorded the same valueInstrument P is more precise because it has a smaller percentage errorInstrument Q is more precise because it rounds to a larger place value