Question

The length of a building is 720 in. Use dimensional analysis to convert this quantity to yards.

Answer 1

20 yards

Explanation:

First, we have to know how to get from inches to yards. 12 inches = 1 foot, and 3 feet = 1 yard.

Next, we have

`(720 in)/(1)`

as a given. We want to multiply this by our conversions to get the end amount in yards.

We can first multiply our expression by 12 inches = 1 foot. To do this, we can set one number as the divisor and one as the dividend, e.g. 12 inches / 1 foot. However, to figure out which number should be the numerator/denominator, we first must examine our original expression. We want to multiply it by a value that cancels something out in conversion. To do this, we can have the same unit of something in the numerator in one and the denominator in the other in terms of what we're multiplying. Here, we can see that
`(720 in)/(1)` has inches on the top, so we want inches on the bottom in 12 inches = 1 foot. Therefore, we have

`(720 in)/(1) * (1 foot)/(12 inches)`

=
`(720feet)/(12)`

= 60 feet

=
`(60 feet )/(1)`

We have feet as the numerator, so we want feet in the denominator in what we're multiplying this by. In 3 feet = 1 yard, we can multiply this to get

`(60 feet )/(1) * (1 yard)/(3 feet) \\= (60 yards)/(3)`

= 20 yards