Question

The micrometer $(\mu \text{m)}$ is often the micron. What the fraction of a centimeter equals $1.0\mu \text{ m?}$

Answer 1

Hint: The micrometer is commonly known as micron. It is an S.I. unit used to calculate length and it is equal to $1\times {10}^{-6}$ meter, that is one millionth of a meter. The micrometer is often used to measure the thickness or diameter of microscopic bodies, such as microorganisms and colloidal particles in a solution.

Complete step-by-step solution:
We are here asked to calculate the fraction of a centimeter equals $1.0\mu m$ .
We already know the relation between a micrometer or micron and a meter (usually denoted by m) which is $1.0\mu m=1\times {10}^{-6}m$.
But we don’t know the relation between a micrometer (micron, denoted as $\mu m$ ) and a centimeter (denoted as cm).
So our first task is to find out the relation between a meter and a centimeter.
As we all know $1$ cm$={10}^{-2}$ m.
i.e. $1$ cm$={\displaystyle \frac{1}{100}}$ m
i.e. $1$ m$=100$ cm.
Which means $1$ m$={10}^2$ cm.
 Now we use the above relation to find the fractional relation between a centimeter and a micron.
We already know $1.0\mu m=1\times {10}^{-6}m$
i.e. $1.0\mu m=1\times {10}^{-6}\times {10}^{2}cm$
i.e. $1.0\mu m=1\times {10}^{-6+2}cm$
i.e. $1.0\mu m=1\times {10}^{-4}cm$
i.e. $1.0\mu m={10}^{-4}cm$
i.e. $1.0\mu m={\displaystyle \frac{1}{10000}}cm$
This is the required fractional between a micron and a centimeter.

Note: This method of changing one unit of a measured quantity to another unit without changing its value is called conversion. For this purpose we have to use a conversion factor. It is widely used in modern physics. The conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, an appropriate conversion factor to an equal value must be used. In this sum, to convert a micron to a centimeter, we used the conversion factor ${10}^{-4}$ .