Least Count

Accuracy and precision are very important in experimental physics and measurements. Any measuring device has a lower limit of measurement, below which it cannot measure or detect values. The minimum value that can be measured is referred to as the Least Count (LC). Knowledge about the least count is necessary in making precise measurements in physics laboratories, particularly when working with instruments such as vernier callipers, screw gauges, and meter scales.

Definition

Least Count of an instrument is the minimum value that can be measured by it with precision. It is the resolving power of the instrument, indicating how finely a measurement can be made.

Formula

Least Count = Value of 1 Main Scale Division / Number of divisions on the scale

Least Count Error

Least count error is the degree of uncertainty of measurement due to the resolution of the instrument. It arises when the reading is between two scale divisions and the precise value is difficult to ascertain. It is taken as ±1 LC.

For instance, if the least count of a vernier calliper is LC = 0.1 mm, then every measurement done has an error of ±0.1 mm.

Minimising Least Count Error

Utilise instruments with a lower least count.
Measure several times and find the average.
Practice proper instrument handling and calibration.

Examples and Practice Problems

Example 1

A scale has 10 main scale divisions equal to 1 cm.
Each main scale division = 0.1 cm.
It has 10 divisions on the vernier scale.
Least Count = 0.1 cm ÷ 10 = 0.01 cm = 0.1 mm.

Least Count of Common Measuring Instruments

Instrument	Typical Least Count
Meter Scale	1 mm (0.1 cm)
Vernier Callipers	0.1 mm (0.01 cm)
Screw Gauge (Micrometer)	0.01 mm
Stopwatch (Digital)	0.01 s
Stopwatch (Analog)	0.1 s
Theodolite	1" (one second of arc)
Thermometer (Lab)	0.1 °C
Electronic Balance	0.01 g

Applications

Stopwatch
Meter Scale
Vernier Callipers and Screw Gauge
Fields like Engineering, Medicine, Astronomy, and Scientific Research:

Summing Up

Least count is the smallest value that a measuring instrument can read. It determines the accuracy of the instrument and is a crucial part of experimental physics. A meter scale generally possesses a least count of 1 mm, a vernier calliper has 0.1 mm, and a screw gauge can go up to 0.01 mm.. The lower the least count, the more accurate the measurement. Least count is also associated with error of measurement—least count error—regarded as ±1 LC. Knowledge of the least count assists in the choice of appropriate instruments, minimising errors, and yielding correct results in experiments.

Frequently Asked Questions

Q1. Why is the least count important?

Least count assists in establishing how accurately an instrument can measure a value. It also assists in the calculation of the uncertainty or error of a measurement.

Q2. What is the least count of a vernier calliper?

For a standard vernier calliper, the least count of a normal vernier calliper is 0.1 mm.

Q3.Can an instrument possess a zero least count?

No, all real instruments possess a finite least count. A zero least count would imply infinite precision, which is not feasible practically.