The length of a piece of stick is 1.75m. A girl measured it as 1.80m. Find the percentage error

Analyze the question: The true length is 1.75 m and the measured length is 1.80 m. We need the percentage error.

Concept: Percentage error = (error ÷ true value) × 100% where error = |measured value − true value|

Solution:

Error = 1.80 − 1.75 = 0.05 m

Percentage error = (0.05 ÷ 1.75) × 100%

= (5 ÷ 1.75)%

= (500 ÷ 175)%

= (20 ÷ 7)%

≈ 2.857%

Check against the options:

• A. 28/7 = 4%, which is not correct
• B. 29/7 ≈ 4.14%, which is not correct
• C. 5%, which is not correct
• D. 20/7 ≈ 2.857%, which matches our working

Answer: D

Tip: Percentage error is always divided by the true (actual) value, not the measured one. If you had divided by 1.80, you would have got 2.78%, which is not among the options. Also, simplify fractions early: 0.05/1.75 = 5/175 = 1/35, and 100/35 = 20/7.