Chapter 1, Problem 1CQ

A guidebook describes the rate of climb of a mountain trail as 120 m per kilometer. How can you express this as a number with no units?

To determine

The rate of climb without unit.

Answer to Problem 1CQ

The rate of climb without unit is $0.12$

Explanation of Solution

Write the unit conversion.

$\begin{array}{c}1\text{km}=\left(1\text{km}\right)\left(\frac{1000\text{m}}{1\text{km}}\right)\\ =1000\text{m}\end{array}$

The rate is given as $120\text{m}$ per $1\text{km}$.

$\begin{array}{c}120\text{m/1}\text{km}=\frac{120\text{m}}{\left(1\text{km}\right)\left(\frac{1000\text{m}}{1\text{km}}\right)}\\ =\frac{120\text{m}}{1000\text{m}}\\ =0.12\end{array}$

Thus, the rate of climb without unit is $0.12$.