Question

A paper has an area of 598 square centimeters. What is the paper's area in square inches? Use the following conversion: 1 square inch is 6.5 square centimeters.

Answer 1

`92.0 in.^(2)`

Explanation:

The prompt said to use the conversion 1 square inch to 6.5 square centimeters.

Keeping this in mind, we will divide the value of 598 square centimeters by a ratio of
`6.5cm^(2) : 1 in.^(2)`.

To do this, we will use the following equation:
`(A_(I)) = (598)/(6.5) (cm^(2))/(cm^(2) /in.^(2) )`

where
`A_(I)` represents the area of the paper in inches.\

Next, divide the numerical value of 598 by 6.5, receiving the quotient
`(598)/(6.5) (cm)/(cm/in.^(2) ) = 92.0 (cm)/(cm/in.^(2) )`.

Now we can adjust to find the proper units.

Cancel the
`cm^(2)` (square centimeters unit) existing in both the numerator and the denominator, thereby leaving
`92.0 (1)/(1/in.^(2) )`.

Finally, since the inverse of the inverse of a number is that same number itself (
`(1)/(1/b) = b`), we rewrite the measuring units of this quotient as
`92.0 in.^(2)`.

Now our answer is clean and finalized for submission.