Suppose Least Count (LC) for some apparatus say 0.1 . But often we used to write 0.1/2 as least count. How this factor "1/2" come into the picture of LC ? We cannot able to measure anything beyond LC by definition. Then why this "1/2" ? Off topic but if you know the answer, please share so that I can understand it clearly...
I'm not sure I fully understand the question, but I think the 1/2 is to account for the fact that the LC is the minimum measurable change in the instrument, but this covers the total range of error. Which effectively means the measurement is the value +/- LC/2.
@Robert Apsimon: Could you tell in detail "Cover the total range of error => +- LC/2".. Why cant it be something else like "LC/3" etc..??
Dear Prasanth,
What I meant is that the TOTAL error is LC, but if you take a measurement, say 1, and the LC is 0.1, then this is equivalent to saying that the measurement is 1 +/- 0.05. This is because on a measurement, the error means that the real value could be more than or less than the measured value.
@ Robert Apsimon, I agree what you have said. But could you tell me what is the physical meaning in reporting a result with an error which is less than the LC ?
Anyhow, we can measure only upto LC not below, right?
You are not reporting a result with a smaller error than the LC. If your least count is 0.1, then you measure a value of 1, then the real value could be anywhere between 0.95 and 1.05, otherwise your apparatus will measure 0.9 or 1.1. The apparatus is effectively using the round function (as opposed to the floor or ceiling functions).
You can measure a value of 0, which really means a value between -0.05 and +0.05, but there is no physical meaning. If you takes lots of measurements of the same quantity then the error will decrease by a factor of 1 / sqrt( n )
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