Practice Questions
Concept Explanation
Error percentage measures how far a measured or estimated value deviates from the true value.
Formula
Percentage error = (|Error|/True value) × 100, where Error = Measured − True (or vice versa depending on context).
Exam Convention
Most placement questions use true value as the base in the denominator unless stated otherwise.
Applied Measurement
If a length is measured 5% too long, and used to compute area, area error is approximately 10% (for small errors, area error ≈ 2 × length error).
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Q1 EasyTrue value is 200 and measured value is 210. Percentage error (based on true value) is:ExplanationError = 10. Percentage error = (10/200) × 100 = 5%.
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Q2 EasyA shopkeeper uses a weight that measures 950 g instead of 1 kg. Percentage error is:ExplanationError = 50 g on true 1,000 g → 5%.
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Q3 EasyThe actual length is 80 cm and measurement is 76 cm. Percentage error is:ExplanationError = 4. Percentage = (4/80) × 100 = 5%.
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Q4 EasyTrue radius is 10 cm but taken as 10.5 cm. Percentage error in radius is:ExplanationError = 0.5 on 10 → 5%.
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Q5 EasyIf measured value is 5% less than true value, percentage error is:ExplanationMeasured = 0.95 × true. Error = 5% of true value.
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Q6 EasyPercentage error when 990 is taken instead of 1,000 is:ExplanationError = 10 on 1,000 → 1%.
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Q7 MediumA student estimated 520 instead of actual 500. Percentage error is:ExplanationError = 20. Percentage = (20/500) × 100 = 4%.
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Q8 MediumIf percentage error is 2.5% and true value is 400, the measured value could be:Explanation2.5% of 400 = 10. Measured = 410 or 390; 410 is listed.
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Q9 MediumA clock loses 6 minutes per hour. Percentage error in time measurement over 1 hour is:ExplanationError = 6 min in 60 min → 10%.
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Q10 HardA student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?ExplanationCorrect = (5/3)x, wrong = (3/5)x. Error% = [(5/3 − 3/5)x / (5/3)x] × 100 = 64%.
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Q11 HardAn error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:ExplanationSide read as 102 instead of 100. Area error = (102² − 100²)/100² × 100 = 4.04%.
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Q12 HardInstead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained?ExplanationCorrect = 7x, wrong = x/7. Error% = (48x/7)/(7x) × 100 = 48/49 × 100 ≈ 97.96%.
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Q13 HardUsing radius with 5% excess, approximate percentage error in area is:ExplanationArea uses r². Approximate area error ≈ 2 × 5% = 10%.
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Q14 HardAn article is counted as 480 instead of 450. Percentage error is:ExplanationError = 30. Percentage = (30/450) × 100 = 6.67%.
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DS1 Easy
A quality inspector checks whether a machine's output meets tolerance limits. What is the percentage error in the measurement?
Statement IThe true (accepted) value of the component length is 500 mm.
Statement IIThe machine recorded a measured value of 525 mm.
ExplanationError = 25 mm. Percentage error = (25/500) × 100 = 5%. Both the true value and measured value are required. -
DS2 Medium
A lab technician reports a reading with a known error rate. What is the measured value?
Statement IThe true value of the sample is 400 units.
Statement IIThe percentage error in the reading is 2.5% based on the true value.
Explanation2.5% of 400 = 10. Measured value = 410 (assuming positive error). Both statements are needed.
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DS3 Medium
An architect verifies a site measurement against the blueprint. Is the percentage error greater than 5%?
Statement IThe actual length of the wall is 80 cm.
Statement IIThe surveyor's measurement recorded 76 cm.
ExplanationError = 4 cm. Percentage error = (4/80) × 100 = 5%, which is not greater than 5%. Both values are needed to decide. -
DS4 Hard
A student's calculator gave a wrong result due to entering the wrong operation. What is the true value?
Statement IThe calculator displayed 210 as the result.
Statement IIThe percentage error is 5% when calculated based on the true value (measured value exceeds true value).
ExplanationTrue value × 1.05 = 210 → true value = 200. Both the displayed result and error rate are needed.