Question

Why can two conversion factors be written for an equality such as $1\mathrm{m}=100\mathrm{cm}$?

Short answer

Two conversion factors can be written for $1\mathrm{m}=100\mathrm{cm}$due to prefix modifier equality.

Step-by-step solution

Given information

We are given that $1\mathrm{m}=100\mathrm{cm}$. We have to prove why there are two conversion factor for this.

Simplify

The prefix modifier equality $1\mathrm{m}=100\mathrm{cm}$can be used to relate metres (m) and centimetres (cm).

Now, $\frac{1\mathrm{m}}{100\mathrm{cm}}=\frac{100\mathrm{cm}}{100\mathrm{cm}}=1$
As a result, the aforementioned equality can be represented as two conversion factors:
$\frac{100\mathrm{cm}}{1\mathrm{m}}$and $\frac{1\mathrm{m}}{100\mathrm{cm}}$