QUESTION

# 1 micron is equal to $\dfrac{1}{{1000000}}m$ which is equal to $1 \times {10^{ - m}}$ meters. The value of m is:

Hint: In order to find the value of m, first we will try to make the given term in the form of power of 10 then by comparing it with the given term we will get the answer.

Given statement “1 micron is equal to $\dfrac{1}{{1000000}}m$ which is equal to $1 \times {10^{ - m}}$ meters”
$\therefore 1{\text{ micron}} = \dfrac{1}{{1000000}}{\text{ meters}}$
We know that 1000000 can be written as ${10^6}$
$1{\text{ micron}} = \dfrac{1}{{{{10}^6}}}{\text{ meters}}$
As we know that $\left[ {\dfrac{1}{{{x^a}}} = {x^{ - a}}} \right]$
$\Rightarrow 1 \times {10^{ - 6}}\,{\text{meters}}$
By comparing the above term with the given term as $1 \times {10^{ - m}}$ meters, we get
$m = 6$