KJSEA 2025 Maths Q14 — Percentage Error in an Estimate

KJSEA 2025 Grade 9 Measurement

Published

The Question

“Salome estimated the height of a window to be 1.5 m. She then measured it and found the actual height was 1.2 m. Which calculation gives the percentage error in her estimate?”

1

Find the error

The error is simply how far the estimate was from the true value. Subtract the actual measured height from the estimated height to see the size of the mistake. Because the estimate was larger than the true value, the difference is positive.

Error=1.5−1.2=0.3 m\text{Error} = 1.5 - 1.2 = 0.3 \text{ m}
2

Recall the percentage error rule

Percentage error compares the size of the mistake to the true value, not to the guess. So you divide the error by the actual value and then multiply by one hundred to turn the fraction into a percentage.

Percentage error=ErrorActual value×100%\text{Percentage error} = \frac{\text{Error}}{\text{Actual value}} \times 100\%

The most common trap is dividing by the estimate. Always divide by the actual (measured) value.

3

Substitute the values

Put the error of 0.3 on top and the actual value of 1.2 underneath, then multiply by one hundred percent. This matches the calculation shown in option B.

0.31.2×100%\frac{0.3}{1.2} \times 100\%

Final Result

The correct calculation is 0.3 divided by 1.2, then multiplied by 100 percent (option B). Working it out gives a percentage error of 25 percent.

Why this method works

Percentage error tells you how big a mistake is relative to the true amount, which is why the actual value must be the denominator. Dividing by the true value 1.2 rather than the estimate 1.5 keeps every measurement judged against reality, so estimates can be fairly compared no matter their size. Multiplying by 100 just rescales the fraction into the percentage form the question asks for.

✓

0.3 ÷ 1.2 = 0.25, and 0.25 × 100% = 25%, a sensible percentage for a 0.3 m miss on a 1.2 m window.