Page 6 Textbook Benchmarks:
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Section 1.3.3 Setup
Measurements with Experimental Error
Enter readings with instrument uncertainty: Value ± ΔValue
Measurement 1 (e.g., Length l)
± 0.6% error
Operation
Measurement 2 (e.g., Breadth b)
± 1.0% error
Measurement Unit:
NCERT Physics Page 6
Example 1.1 & 1.2 Solvers
Section 1.3.3 Observation (2)
12.9 g − 7.06 g = 5.8 g
Why Subtraction Reduces Significant Figures
The textbook highlights that while combining experimental data usually maintains n significant figures, subtracting two nearly equal measurements drastically reduces the number of significant figures. This is because addition and subtraction obey the smallest number of decimal places, NOT the number of significant figures!
3 Significant Figures | 1 decimal place
−
3 Significant Figures | 2 decimal places
Section 1.3.3 Observation (3)
1.02 g (±1%) vs 9.89 g (±0.1%)
Relative Error Depends on the Number Itself, Not Just Significant Figures
Both numbers below are measured with the exact same precision (± 0.01 g) and have the exact same count of significant figures (3 Significant Figures). Yet, their relative percentage error differs by a factor of 10!
Measurement 1: 1.02 g
± 0.01 g
Relative Error = (± 0.01 / 1.02) × 100%
= ± 0.98% ≈ ± 1.0% error
High relative uncertainty (1 part in 100)
Measurement 2: 9.89 g
± 0.01 g
Relative Error = (± 0.01 / 9.89) × 100%
= ± 0.101% ≈ ± 0.1% error
Ten times more accurate (1 part in 1000)
💡 Key Takeaway from Page 6: You cannot judge the percentage accuracy of an experimental measurement solely by counting its significant figures. The magnitude of the measurement itself directly dictates its relative error!