If the cost per minute is $\$0.032$, is the cost per hour $\$1.92$ or $1.92$¢?

Question

I hope someone can help me with this problem. The cost per minute to make a phone call is $0.032, I'm that multiplying this by 60 will get total cost per hour.

$0.032 * 60 = 1.92 

I'm not sure if that is a $1.92 or 1.92 ¢

Thank you

Answer 1

Units act like special numbers multiplicatively:

$$\$0.032 = 0.032\ \textrm{dollars}.$$

The cost of a phone call is $$0.032 \frac{\textrm{dollars}}{\textrm{minute}}.$$

The cost of a 60 minute call is then

$$\require{cancel}\textrm{cost} = 0.032 \frac{\textrm{dollars}}{\cancel{\textrm{minute}}} \cdot 60\ \cancel{\textrm{minute}} = 60 \cdot 0.032\ \textrm{dollars} = 1.92\ \textrm{dollars}.$$

If we want to convert to cents, we multiply by the conversion factor:

$$1.92\ \cancel{\textrm{dollars}} \cdot \frac{100\ \textrm{cents}}{\cancel{\textrm{dollar}}} = 192\ \textrm{cents}.$$