# If 10^-3 m is 1 mm, then 10^-6 m is 2 mm, isn’t it?

Mathematics TSWREIS, Narsingi (State Board) Narsingi, Hyderabad , Telangana Class 12 24 June, 2017

This is a common question that students have but are ashamed to ask.

As per your logic, $1mm={10}^{-3}m$

Multiplying both sides by 2 to maintain equality we get

$2×1mm=2×{10}^{-3}m$ and not ${10}^{-6}mm$.

Please recall the property of exponents which is as follows....

${a}^{m}×{a}^{n}={a}^{\left(m+n\right)}$ therefore, ${a}^{-m}×{a}^{-n}={a}^{\left(-m-n\right)}$

Applying this property in our example,

${10}^{-6}={10}^{-3}×{10}^{-3}$=${10}^{\left(-3-3\right)}={10}^{-6}$

So,

$\begin{array}{l}{10}^{-6}m={10}^{-6}×1m\\ ={10}^{-6}×{10}^{+3}mm\left[::1m=1000mm\right]\end{array}$

$\begin{array}{l}{10}^{-6}m={10}^{-3}mm\\ =\frac{1}{{10}^{3}}mm=\frac{1}{1000}mm\end{array}$

Anand Kurien

Author

H.S. Mani

Author

Do you think you can improve this answer? Learn how to submit a new answer