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$ = \dfrac{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. $1.0\mu m = \dfrac{1}{{10000}}cm$
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 ${10^{ - 4}}$ .