Q. 2.43 - An Introduction to General, Organic, and Biological Chemistry

Question

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

Step-by-Step Solution

Answer

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

Step 1 : Given information

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

Step 2 : 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 $\frac{1 \mathrm{m}}{100 \mathrm{cm}}$