# Measuring through meter scale

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.

• You cannot. Metre scale cannot give that accuracy. – Wrichik Basu Aug 6 '17 at 13:24

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.
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.