MSR = 0.9 cm, n = 6, LC = 0.01 cm
Total = MSR + n × LC = 0.9 + 6 × 0.01 = 0.9 + 0.06 = 0.96 cm
The Vernier caliper uses the Vernier principle to measure lengths more precisely than a simple ruler. The main scale (fixed) measures to 1 mm precision. The Vernier scale (sliding) divides the smallest main scale division into smaller parts. N Vernier divisions = (N−1) main scale divisions. So 1 VSD = (N−1)/N × 1 MSD. Least count = 1 MSD − 1 VSD = 1/N MSD. For N=10: LC = 0.1 mm. The Vernier scale division that coincides with a main scale division tells you the fractional part beyond the main scale reading.
Metre scale: LC = 1 mm (0.1 cm). Vernier caliper: LC = 0.1 mm (0.01 cm). Screw gauge (micrometer): LC = 0.01 mm (0.001 cm). Spherometer: LC = 0.01 mm. Travelling microscope: LC = 0.001 cm. The precision increases by 10× with each instrument. For NEET, remember: Vernier caliper = 0.1 mm = 0.01 cm precision; Screw gauge = 0.01 mm = 0.001 cm precision.
For comparison: Screw gauge total reading = MSR + (circular scale division × LC). LC of screw gauge = Pitch / Number of circular scale divisions. Pitch = distance moved per full rotation = usually 1 mm. Number of circular divisions = 100. So LC = 1/100 mm = 0.01 mm. MSR = reading on linear scale (in mm). Total = MSR + (circular division × 0.01 mm).
Systematic error: consistently in one direction (zero error, calibration error). Random error: unpredictable fluctuations. Percentage error = (absolute error / true value) × 100. Combination of errors: if Z = A + B: ΔZ = ΔA + ΔB. If Z = A × B or A/B: ΔZ/Z = ΔA/A + ΔB/B. If Z = Aⁿ: ΔZ/Z = n × ΔA/A.