Least count
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Least count is the highest degree of accuracy of measurement that can be achieved. For example the least count of a voltmeter is the minimum change that can be discerned. The formula is - Range/number of divisions.
Every measuring instrument has error when readings are taken. The least count, uncertainty or maximum possible error characterize such errors.
Instruments' errors can be compared by calculating the percentage of uncertainty of their readings. The instrument with the least uncertainty is taken to measure objects, as all measurements consider accuracy. The percentage uncertainty is calculated with the following formula:
- (Maximum Possible error/Measurement of the Object in question) *100
The smaller the measurement, the larger the percentage uncertainty. The least count of an instrument is inversely proportional to the precision of the instrument.
A Vernier scale is constructed by taking 49 main scale divisions dividing them into 50 divisions
- ie. 49mm divided into 50 parts
- therefore
- 1 vsd=49/50 mm=0.98mm
- 1 MSD=1mm
- substituting in formula
- L.C = 1 M.S.D - 1 V.S.D
Least count error
The smallest value that can be measured by the measuring instrument is called its least count. Measured values are good only up to this value. The least count error is the error associated with the resolution of the instrument.
For example, a vernier caliper's least count is 0.02 mm while a micrometer may have least count of 0.01,spherometer may have a least count of 0.002 mm. Least count error belongs to the category of random errors but within a limited scale; it occurs with both systematic and random errors. If we use a metre scale for measurement of length, it may have graduations at 1 mm division scale spacing or interval.
Instruments of higher precision, improving experimental techniques, etc., can reduce the least count error. Repeating the observations and taking the arithmetic mean of the result, the mean value would be very close to the true value of the measured quantity.-
Least count is the least unit that a measuring instrument can measure.
It is given by value of smallest division on main scale divided by total number
of divisions on vernier scale.