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What if the measuring thing is found to have length between 6mm and 7mm. Like u r measuring the length of an object which has the length between 5.6cm and 5.7 cm. The millimeter distance was between somewhere of 6 mm and 7 mm. How can I deduce the distance?

Note: I am just using meter scale. Not Vernier Caliper.

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    $\begingroup$ You cannot. Metre scale cannot give that accuracy. $\endgroup$ – Wrichik Basu Aug 6 '17 at 13:24
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  1. In a single measurement with a ruler, you can not tell $0.1~mm$ apart, but you can certainly do better than $1~mm$. By eyeballing, I would say that a standard deviation $\sigma~\sim~0.2~mm$ is not unrealistic.

  2. If you repeat the measurement sufficiently many times, you are able to statistically deduce one extra digit beyond the millimeters.

  3. The trick is to not put one end of the object at $0~mm$ on the ruler: Place instead the ruler arbitrary along the object, and write down the readings $XX.X~mm$ and $YY.Y~mm$ at each end, eyeballing the last digit. The length is then $(YY.Y-XX.X)~mm \pm \sigma\sqrt{2}$.

  4. Slide the ruler arbitrarily along the object. Repeat measurement $n$ times. Take the average. The resulting standard deviation $\sim \sigma\sqrt{2/n}$ is now well into the sub-millimeter range.

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