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

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A sports equipment manager in Brisbane estimates that 28 basketballs and 46 footballs are needed for a regional tournament. The actual number required, confirmed by a detailed inventory analysis, is 25 basketballs and 44 footballs.

Calculate the percentage error in the total number of balls using the formula: percentage error = |estimated total - actual total| / actual total × 100. Give the exact result as a simplified fraction.

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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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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The estimated number of basketballs is 28 and footballs is 46, so the estimated total number of balls is 28 + 46 = 74.
  2. The actual number of basketballs is 25 and footballs is 44, so the actual total number of balls is 25 + 44 = 69.
  3. Calculate the absolute difference between the estimated total and actual total: |74 - 69| = 5.
  4. Divide the absolute error by the actual total: 5 / 69.
  5. Multiply the result by 100 to convert to a percentage: (5 / 69) × 100.
  6. Perform the division: 5 ÷ 69 = 5/69.
  7. Multiply 5/69 by 100: (5 × 100) / 69 = 500 / 69.
  8. Simplify the fraction 500/69. The greatest common divisor of 500 and 69 is 1, so the fraction is already in simplest form.
  9. The percentage error is 500/69 %.
  10. Verify the calculation: 500 ÷ 69 ≈ 7.246, and 7.246% of 69 is approximately 5, which matches the error. The calculation is correct.
  11. The percentage error in the total number of balls is exactly 500/69 %.
  12. The final answer is 500/69 %, which is the exact simplified fraction.

Reference answer: 500/69 %

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