Year 9 Maths • AC9M9M04 • Authored homework
Error, accuracy and percentage error
Calculate and interpret absolute error, relative error and percentage error in practical measurement contexts. Explain what the error means and whether it is acceptable. Show working, use correct units or notation, and check reasonableness.
Part A
Short-answer questions
Define absolute error.
Define relative error.
Write the percentage error formula.
A measured length is 24 cm but the true length is 25 cm. Find the absolute error.
Using the same values, find the percentage error.
Explain why percentage error can be more useful than absolute error when comparing measurements.
Round 8.764 to 2 decimal places and state the possible rounding error.
What is the difference between precision and accuracy?
Correct this error: percentage error = true value ÷ error × 100.
Give one situation where a small measurement error could matter.
Part B
Long-answer questions
A student measures a table as 1.18 m. The true length is 1.20 m. Calculate absolute error, relative error and percentage error.
Compare a 2 cm error in a 20 cm measurement with a 2 cm error in a 200 cm measurement. Which is more serious and why?
A scale has readings to the nearest 0.1 kg. Explain the maximum possible rounding error for one reading.
A class estimates a distance as 48 m when the actual distance is 52 m. Calculate percentage error and interpret it.
Explain how repeated measurements can reduce the effect of random error but not always remove systematic error.
A recipe uses 500 g of flour but a student uses 465 g. Calculate the percentage error and discuss whether it might matter.
A phone GPS reports a 5.0 km run as 4.8 km. Calculate percentage error and explain the impact on pace estimates.
Create a measurement table with true value, measured value, absolute error and percentage error for three items.
Evaluate whether it is better to report a measurement as 3 m, 3.0 m or 3.00 m in a given context.
Write a full worked response for a practical error problem, including formula, substitution, answer and interpretation.
Part C
Research and understanding task
Find a real measurement context, such as sport timing, cooking, construction, medicine, GPS, science practicals or manufacturing. Explain possible sources of error and calculate a sample percentage error.