Measuring Instruments And Least Count

The least count of a vernier caliper is the smallest length it can resolve, found from the difference between one main-scale division and one vernier-scale division. Since ten vernier divisions span the same length as nine main-scale divisions, one vernier division equals 9/10 of a main-scale division. With the smallest main-scale division being 1 mm, one vernier division measures 0.9 mm. The least count is therefore 1 MSD minus 1 VSD = 1 mm - 0.9 mm = 0.1 mm, which equals 0.01 cm. The choice 0.1 cm equals one whole millimetre, the main-scale division itself, and ignores the vernier refinement. The choice 0.001 cm would require a hundred vernier divisions matching ninety-nine main divisions, which is not the case here. The choice 1 mm simply restates the main-scale division and is not a least count at all. This is precisely the standard formula least count = value of one main-scale division divided by the number of vernier divisions. As a check, dividing 1 mm by 10 vernier divisions gives 0.1 mm, confirming 0.01 cm.