Significant figures and percentage error: Class 11 practice
Results of multiplication/division keep as many significant figures as the least precise value. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Percentages
The idea behind significant figures and percentage error
Results of multiplication/division keep as many significant figures as the least precise value. Percentage errors add when quantities are multiplied or divided, and are multiplied by the power when raised to a power.
Step-by-step method
- Count significant figures (non-zero digits, zeros between them, trailing zeros after a decimal point).
- For Z = AᵖBᑫ, %Z = p%A + q%B.
- Round the answer sensibly.
Worked example 1 (Basic)
How many significant figures are in 0.00450?
- Ignore leading zeros; count others (trailing zeros after a decimal count)
- Answer: 3
Worked example 2 (Standard)
Z = A × B with A known to ±2% and B to ±4%. Find the percentage error in Z.
- %Z = 2 + 4
- Answer: ±6%
Worked example 3 (Challenge)
Z = A^2/B with A known to ±2% and B to ±1%. Find the percentage error in Z.
- %Z = 2 × 2 + 1
- Answer: ±5%
Common mistakes and misconceptions
- Counting leading zeros
- Subtracting errors in a quotient
Practice questions
- (Basic) How many significant figures are in 6.022?
- (Basic) How many significant figures are in 1200?
- (Standard) Z = A × B with A known to ±3% and B to ±5%. Find the percentage error in Z.
- (Standard) Z = A × B with A known to ±1% and B to ±4%. Find the percentage error in Z.
- (Challenge) Z = A^2/B with A known to ±5% and B to ±3%. Find the percentage error in Z.
- (Challenge) Z = A^3/B with A known to ±1% and B to ±1%. Find the percentage error in Z.
Answer key with full working
- Q1: Ignore leading zeros; count others (trailing zeros after a decimal count) → Answer: 4
- Q2: Ignore leading zeros; count others (trailing zeros after a decimal count) → Answer: 2
- Q3: %Z = 3 + 5 → Answer: ±8%
- Q4: %Z = 1 + 4 → Answer: ±5%
- Q5: %Z = 2 × 5 + 3 → Answer: ±13%
- Q6: %Z = 3 × 1 + 1 → Answer: ±4%
Syllabus note
This skill is listed under "Units and Measurements" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is significant figures and percentage error in?
"Units and Measurements", Class 11 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.