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For a measurement of 4.6 (between 4.6 and 4.7 ) with a least count of 0.1 we write the measurement as 4.6 ± 0.1 . Why can't we write it as 4.65 ± 0.05. My guess is this gives a false sense of resolution of the instrument. I would like a nice explanation. 6 is uncertain here.

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Yes! You are right. When your instrument has a resolution of $0.1$, How come you able to measure up to two-digit after the decimal point.

It's like, You have measured in millimeter with centimeter stick.

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The reason is that, since your instrument only measures in steps of $0.1$ of some unit (say, millimeters), any measurement could be off by less than that amount without your instrument being able to correctly capture it, leading to an error. Since $\pm \, 0.1\, $mm is the largest possible range of this kind of error, that is what you should report.

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