Significant Figures
In the measured value of a physical quantity, the digits about which we are certain, together with the first doubtful digit, are called significant figures.
The greater the number of significant figures in a measurement, the higher the accuracy of the measurement.
Accuracy and Precision
Accuracy describes how close a measured value is to the true or accepted value of a quantity.
Precision refers to the resolution or degree of detail to which a measurement is made, regardless of whether it is close to the true value.
Least Count
The least count (LC) of a measuring instrument is the smallest value that the instrument can measure accurately. It represents the resolution of the instrument.
Least Count-Example
| Instrument | Formula for Least Count |
|---|---|
| Vernier Callipers |
LC =
Value of 1 main scale division ÷ Total number of vernier scale divisions |
| Screw Gauge |
LC =
Value of 1 pitch scale reading ÷ Total number of head scale divisions |
Vernier Caliper — Worked Example
1) Find the Least Count (LC)
- Value of 1 main scale division (MSD) = 1 mm
- Total vernier divisions (VD) = 10 (standard vernier)
For a standard vernier, LC = (value of 1 MSD) ÷ (number of vernier divisions) = 1 mm ÷ 10 = 0.1 mm (i.e., 0.01 cm).
2) Take a Measurement (no zero error)
- Main scale reading just before the vernier zero (MSR) = 24 mm
- Vernier coincidence = 7th division
Vernier reading = (coinciding division) × LC = 7 × 0.1 mm = 0.7 mm
Observed length = MSR + Vernier reading = 24 mm + 0.7 mm = 24.7 mm
3) Zero-Error Correction (if present)
Suppose when the jaws are fully closed, the vernier zero lies to the right of the main scale zero by 2 divisions (i.e., zero error = +0.2 mm).
- Positive zero error → subtract correction from observed value.
- Negative zero error → add correction to observed value.
True length = 24.7 mm − 0.2 mm = 24.5 mm
Screw Gauge — Worked Example
1) Find the Least Count (LC)
- Pitch = linear advance of the spindle in one full rotation = 0.5 mm
- Number of head (circular) scale divisions = 50
LC = Pitch ÷ number of head divisions = 0.5 mm ÷ 50 = 0.01 mm (i.e., 10 μm).
2) Take a Measurement (no zero error)
- Pitch scale (sleeve) reading, PSR = 5.5 mm
- Head (circular) scale reading, CSR = 23 divisions
Circular contribution = CSR × LC = 23 × 0.01 mm = 0.23 mm
Observed diameter = PSR + circular contribution = 5.5 mm + 0.23 mm = 5.73 mm
3) Zero-Error Correction (if present)
Suppose when the anvils just touch (zero), the head scale reads +4 divisions (zero error = +4 × 0.01 mm = +0.04 mm).
- Positive zero error → subtract correction from observed.
- Negative zero error → add correction to observed.
True diameter = 5.73 mm − 0.04 mm = 5.69 mm
Quick Rules
- Vernier Caliper reading = MSR + (Vernier coincidence × LC)
- Screw Gauge reading = PSR + (CSR × LC)
- Apply zero-error correction at the end: Positive zero error → subtract; Negative zero error → add.