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

Analyze the question: The true length is 1.75 m and the boy's measurement 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 ÷ 175) × 100%

= (1 ÷ 35) × 100%

= 100/35 %

= 20/7 %

= 2 6/7 %

Check: 20 ÷ 7 = 2 remainder 6, so 2 6/7. ✔

Comparing with the options:

• A. 4 4/7: no
• B. 2 6/7: matches
• C. 2 7/9: no
• D. 4 7/9: no

Tip: In percentage error questions, always divide by the true (actual) value, not the measured one. If you divided by 1.80 instead, you would get 2 7/9 % (option C), which is a common trap. Also simplify the fraction early: 0.05/1.75 = 1/35 makes the arithmetic quick.