Question

A micron is related to centimetre as:
A) $1$ micron $ = {10^{ - 8}}cm$
B) $1$ micron $ = {10^{ - 6}}cm$
C) $1$ micron $ = {10^{ - 5}}cm$
D) $1$ micron $ = {10^{ - 4}}cm$

Answer 1

Hint: Prefixes of units define different orders of magnitude of the same unit. That means that as long as the unit is the same, the units can be interchanged with a change in their numerical values.

Complete step by step answer:
Every unit has some predefined prefixes that intend to signify the order of magnitude of that physical quantity. Those magnitudes can be macroscopic as well as microscopic, and have prefixes denoted accordingly.
Micron is another name for micrometre $\left( {\mu m} \right)$. Here the base unit is metre $\left( m \right)$ and the prefix is micro $\left( \mu \right)$. Its exponential value can be given as,
$1\mu m = {10^{ - 6}}m$, which can also be written as
$1m = {10^6}\mu m$..........[equation $1$]
Also, $1cm = {10^{ - 2}}m$, which can also be written as
$1m = {10^2}cm$..................[equation $2$]
Dividing equation $1$ and $2$,
$\Rightarrow \dfrac{{1m}}{{1m}} = \dfrac{{{{10}^6}\mu m}}{{{{10}^2}cm}}$
$ \Rightarrow {10^4}\dfrac{{\mu m}}{{cm}} = 1$
$\therefore 1\mu m = {10^{ - 4}}cm$

Thus, option D is the correct answer.

Note: Micron is a unit of length that is used to measure thickness of a wire, length of a macromolecule, intercellular distances, size of a cell etc. Whereas centimetre is a unit of length used to measure distances on a map, lengths and width of two dimensional shapes etc.