Why do values of conversion factors equal one?

Answer 1

The whole point of converting one quantity to another is that the value that

you start with and the value that you end with must be equal.

There's only one thing you can multiply the first value by, without changing it

into something different, and that's ' 1 '. If you multiply it by anything else,

you'll change it, and it won't be equal to whatever you end up with.

You can multiply anything you want to by (1-foot/12-inches) or by (7-days/1-week),

or by (1-day/24-hours), because those are all equal to ' 1 '.

Answer 2

Conversion factors are constructed in such a way that the value of the numerator unit is equivalent to the value of the denominator unit. This means that when the units are multiplied or divided together, they cancel out, resulting in a value of one. This property allows us to convert from one unit to another without changing the actual quantity being measured.