Question

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

Answer 1

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.

Complete step-by-step 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 \[{10^6}\]
So, by substituting the value of 1000000, we have
$1{\text{ micron}} = \dfrac{1}{{{{10}^6}}}{\text{ meters}}$
As we know that $\left[ {\dfrac{1}{{{x^a}}} = {x^{ - a}}} \right]$
By using this property, we have
$ \Rightarrow 1 \times {10^{ - 6}}\,{\text{meters}}$
By comparing the above term with the given term as $1 \times {10^{ - m}}$ meters, we get
$m = 6$
Hence, the value of m is 6.

Note: In order to solve these types of questions related to exponents, learn all the properties of exponents. Also learn the concept of units and dimensions such as 1meter can be represented as 100cm. Similarly learn about millimeters, micrometers, nanometers and many more terms like this. This will be quite helpful in solving many problems like this.