NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Measurement errors

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A school in Adelaide orders 35 boxes of science lab equipment, each containing 14 identical test tubes. The supplier delivers 490 test tubes in total.

The actual number required, based on the order, is 490. Calculate the percentage error in the delivered quantity using the formula: percentage error = |measured value - actual value| / actual value × 100.

Give the exact result as a simplified fraction.

Concept illustrations

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Measurement compared with a reference. Measured length 49 cm differs from the reference 50 cm by 1 cm. Absolute error is 1 cm and percentage error is 2%. The axis is a close-up from 48 to 51 cm.48 cm49 cm50 cm51 cmMeasured: 49Reference: 50|49 − 50| = 1 cm
Measured length 49 cm differs from the reference 50 cm by 1 cm. Absolute error is 1 cm and percentage error is 2%. The axis is a close-up from 48 to 51 cm.
Nearest hundredth on a number line. 6.347 lies between 6.34 and 6.35. It is beyond the midpoint 6.345, so rounding to the nearest hundredth gives 6.35.6.346.3456.356.3476.347 ≈ 6.35
6.347 lies between 6.34 and 6.35. It is beyond the midpoint 6.345, so rounding to the nearest hundredth gives 6.35.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The actual number of test tubes required is 35 boxes × 14 test tubes per box = 490 test tubes.
  2. The supplier delivered 490 test tubes, so the measured value is 490.
  3. The actual value is 490, and the measured value is 490, so the difference is |490 - 490| = 0.
  4. Substitute into the percentage error formula: |measured - actual| / actual × 100 = 0 / 490 × 100.
  5. 0 divided by 490 is 0.
  6. 0 multiplied by 100 is 0.
  7. The percentage error is 0%.
  8. Express 0 as a simplified fraction: 0/1.
  9. The fraction 0/1 is already simplified.
  10. Check: since measured value equals actual value, error is zero, so percentage error must be 0.
  11. The percentage error is exactly 0, which as a simplified fraction is 0/1.
  12. Final answer: 0/1.

Reference answer: 0/1

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