Question

A particular beach is eroding at a rate of 4 centimeters per year. A realtor converts this rate to millimeters per day. Which

expression, when evaluated, results in the correct units and numerical value?

Answer 1

Its A

Explanation:

Answer 2

`(4cm)/(1year)*(10mm)/(1cm)*(1year)/(365days)`

Explanation:

Whenever we are doing unit conversions, we have to remember to make the first ratio and then each successive ratio should be put in such a way that the top and bottom cancels out with each unit and whatever we want, remains.

A simple example would be if we were to just convert from cm to mm. Suppose we want to convert 5 centimeters to millimeters. We can write the ratios is 2 ways:

First:

`5cm*(10mm)/(1cm)`

Second:

`5cm*(1cm)/(10mm)`

The first one is correct since we want mm, mm should be on top and cm should be on bottom form cm and cm to get canceled.

Now, for our problem, we want mm on top and day on bottom. So, cm and year should cancel. Looking at the first choice, the conversion factors are correct & skimming through, we see that

cm and cm cancels (top and bottom), also year and year cancels (top and bottom), it will leave us with mm on top and days on bottom, which is what we want.

First answer choice is right.