Re: how do you convert inches to meters?

You start with the facts that 1 in = 2.54 cm,
and 100 cm = 1 m

So, if you start with inches, first multiply by 2.54 cm/in to get centimeters, and then multiply by 0.01 m/cm to obtain meters.

There is a general principle here that will help you to convert any unit to any other unit of the same type. That principle is that at each multiplication you are multiplying by one! And you know that multiplying by one does not change the answer. What it does change is the units.

Notice that the first multiplier is 2.54 cm/in. That is, the numerator is 2.54 cm, and the denominator is 1 in, and since those two distances are an equivalent distance, the fraction 2.54 cm divided by 1 inch is actually the fraction "one"!! You can construct any unit-changing multiplier as long as the numerator and denominator are equivalent quantities. This applies to units other than length, too, so you can convert time units to other time units, or mass units to other mass units, or.... you get the idea.

Also notice that the unit of the first measurement, inches, is in the denominator of the first multiplier. When we multiply inches by cm/in, we get the fraction "inch times centimeter divided by inch", which, since "inch divided by inch" is one, we are left with centimeters. So, the second multiplier should have centimeters in the denominator. We construct the second multiplier to be equal to "one", as before, but this time the equal quantities are "1 meter" and "100 centimeters". The fraction is "1 meter divided by 100 centimeters", so we get 0.01 m/cm for the second multiplier!

This principle can be strung together with as many unit-changing multipliers as are needed to get to the unit you want. I have often encountered problems in school and at work where I have strung together at least 5 unit-changing multipliers to change from one unit to another.

John Link, MadSci Physicist