Units and Measurements Part 3

Concept:The least count is the smallest measurement that an instrument can read accurately.It is equal to the smallest decimal place common to all recorded readings.Explanation:The given readings are $1.24\,\mathrm{mm}$, $1.25\,\mathrm{mm}$, $1.23\,\mathrm{mm}$, and $1.21\,\mathrm{mm}$.All readings are recorded up to two decimal places (hundredths of a millimeter).The difference between two consecutive readings, e.g., $1.25\,\mathrm{mm} - 1.24\,\mathrm{mm} = 0.01\,\mathrm{mm}$, is $0.01\,\mathrm{mm}$.If the least count were $0.1\,\mathrm{mm}$, readings would have only one decimal place (like $1.2\,\mathrm{mm}$).If the least count were $0.001\,\mathrm{mm}$, readings would have three decimal places (like $1.240\,\mathrm{mm}$).If the least count were $0.05\,\mathrm{mm}$, readings would end only in $.00$ or $.05$ (e.g., $1.20$, $1.25$), but $1.24$ and $1.23$ are present, so it is not possible.Therefore, the smallest unit consistent with all readings is $0.01\,\mathrm{mm}$.Answer:The expected least count is $0.01\,\mathrm{mm}$, which corresponds to option (A).