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 Easy
True value is 200 and measured value is 210. Percentage error (based on true value) is:
ExplanationError = 10. Percentage error = (10/200) × 100 = 5%. -
Q2 Easy
A shopkeeper uses a weight that measures 950 g instead of 1 kg. Percentage error is:
ExplanationError = 50 g on true 1,000 g → 5%. -
Q3 Easy
The actual length is 80 cm and measurement is 76 cm. Percentage error is:
ExplanationError = 4. Percentage = (4/80) × 100 = 5%. -
Q4 Medium
A student estimated 520 instead of actual 500. Percentage error is:
ExplanationError = 20. Percentage = (20/500) × 100 = 4%. -
Q5 Medium
If 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. -
Q6 Medium
A meter scale reads 1% short. The percentage error in measuring a 200 cm cloth is:
ExplanationScale reads 99% of true, so error based on true = 1%. -
Q7 Easy
True 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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Q8 Hard
Using radius with 5% excess, approximate percentage error in area is:
ExplanationArea uses r². Approximate area error ≈ 2 × 5% = 10%. -
Q9 Hard
An article is counted as 480 instead of 450. Percentage error is:
ExplanationError = 30. Percentage = (30/450) × 100 = 6.67%. -
Q10 Easy
If measured value is 5% less than true value, percentage error is:
ExplanationMeasured = 0.95 × true. Error = 5% of true value. -
Q11 Medium
A clock loses 6 minutes per hour. Percentage error in time measurement over 1 hour is:
ExplanationError = 6 min in 60 min → 10%. -
Q12 Easy
True value 250, error 2%. Measured value is:
Explanation2% of 250 = 5. Measured could be 255 (or 245); 255 listed. -
Q13 Easy
Percentage error when 990 is taken instead of 1,000 is:
ExplanationError = 10 on 1,000 → 1%. -
Q14 Medium
If error is 8 and true value is 160, percentage error is:
Explanation(8/160) × 100 = 5%.
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DS1 Easy
What is the percentage error?
Statement ITrue value is 500.
Statement IIMeasured value is 525.
ExplanationError = 25. Percentage = (25/500) × 100 = 5%. Both needed. -
DS2 Medium
What is the measured value?
Statement ITrue value is 400.
Statement IIPercentage error is 2.5%.
ExplanationError = 10. Measured = 410 or 390; with positive error, 410.
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DS3 Medium
Is the percentage error greater than 5%?
Statement ITrue value is 80 cm.
Statement IIMeasured value is 76 cm.
ExplanationError = 5%, which is not greater than 5%. Both true and measured values are needed. -
DS4 Hard
What is the true value?
Statement IMeasured value is 210.
Statement IIPercentage error is 5% based on true value.
ExplanationTrue × 1.05 = 210 → true = 200. Both needed.