5.8 Introduction and Key Insights

We use decimal notation all the time when we make measurements, especially when using the metric system, where quantities are based on measures of ten. Let's return to your aunt's coffee shop for an example, where she is busy designing a new sign to display in the window.

Your aunt is trying to make sense of the measurements for this rectangle, which are expressed as 1.25 m by 0.75 m. She would like to paint her sign white, and knows that one bottle of paint can cover a 50 cm by 50 cm = 2500 cm2 area. How many bottles does your aunt need to paint the entire sign? (Give it a try!)

Probably your first step is to express all of your measurements in the same units. We know that one centimeter equals one-hundredth of a meter, or, in decimal form, that 1 cm = 0.01 m.

Next, we figure out that one bottle of paint will cover $0.5 \times 0.5 = 0.25 m^{2}$ units of area. The area of the sign is given by $1.25 \times 0.75 = 0.9375 m^{2}$, and so the last step in this process is to divide $0.935$ by $0.25$. After doing some work, we find that:

$0.935 \div 0.25 = 3.75$

This tells us that we will need 3 and $3/4$ bottles of paint. Assuming we can only purchase individual bottles, your aunt will need to buy a total of 4.