Topic 5: Significant Figures

What are Significant Figures?

Significant figures are the meaningful digits in a measured quantity. They indicate the precision of a measurement.

Significant figures include:

  • All non-zero digits
  • Zeros between non-zero digits
  • Trailing zeros only if a decimal point is present

Rules for Counting Significant Figures

Rule 1: Non-zero digits

All non-zero digits are significant.

Example: 234 → 3 significant figures

Rule 2: Zeros between non-zero digits

Zeros between non-zero digits are always significant.

Example: 1002 → 4 significant figures

Rule 3: Leading zeros

Zeros before non-zero digits are not significant.

Example: 0.005 → 1 significant figure

Rule 4: Trailing zeros

Trailing zeros are significant only if a decimal point is present.

Example: 150 → 2 significant figures 150.0 → 4 significant figures

Significant Figures in Calculations

Addition & Subtraction

The result should have the same number of decimal places as the least precise value.

Multiplication & Division

The result should have the same number of significant figures as the least precise value.

Rounding Off

If the digit to be dropped is less than 5, leave the preceding digit unchanged. If it is 5 or more, increase the preceding digit by 1.

Q1. Number of significant figures in 0.0045 is:
A) 1
B) 2
C) 3
D) 4
Answer: B

Q2. How many significant figures are there in 1200?
A) 1
B) 2
C) 3
D) 4
Answer: B

Q3. Number of significant figures in 1200.0 is:
A) 2
B) 3
C) 4
D) 5
Answer: C

Q4. Zeros between non-zero digits are:
A) Never significant
B) Sometimes significant
C) Always significant
D) Significant only with decimal
Answer: C

Q5. Result of multiplication should contain:
A) Maximum significant figures
B) Minimum significant figures
C) Average significant figures
D) No significant figures
Answer: B

Significant Figures – Quick Revision

Definition

Significant figures represent the precision of a measurement.

Counting Rules

  • All non-zero digits are significant
  • Zeros between non-zero digits are significant
  • Leading zeros are not significant
  • Trailing zeros are significant only with decimal

Examples

  • 0.006 → 1 significant figure
  • 305 → 3 significant figures
  • 400 → 1 significant figure
  • 400.0 → 4 significant figures

Calculations

  • Add/Subtract → least decimal places
  • Multiply/Divide → least significant figures

Rounding Off Rule

  • < 5 → ignore
  • ≥ 5 → increase previous digit by 1

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