Confused about conversion factors........?

Question

Never really enjoyed math, but I do it anyway. Any advice on learning to do and understand conversion factors? Example:

The distance of a 220. yard race is equivalent to ___ cm.

The answer is 2.01 10^4. How'd they get this?

Answer 1

220yd x 3ft/1yd x 12in/1ft x 2.54cm/1in = 20,116.8cm

There are only two significant figures in 220 yd, so the answer should be rounded to 20,100 cm. And that is 2.01 x 10^4.

Answer 2

Conversion factors are a pain. Think of them this way...

You want equivalent numbers as the numerator and denominator of the conversion factor you set up. (Both the upper number and the lower number equal the same thing, like for instance 12 inches / 1 foot or 1 foot / 12 inches) The one on top and the one on bottom will be set by the conversion you want to do. You will always multiply, so the number on bottom of the conversion factor is the one you want to cancel and the one on top is the one you want to get to (unit cancelation method or dimensional analysis). So for your problem - to get from yards to cm, you would need a factor having the form __ cm / __ yards

I don't know this factor, so we have to work our way to it. We can change yards to feet using 3 feet / 1 yard This gives us feet and we can now use 12 inches / 1 foot This will give us inches and so 2.54 cm / 1 inch (which I found in the book) will give us cm. String it all together and we get:

220 yards (3 feet / 1 yard) (12 inches / 1 foot) (2.54 cm / 1 inch) = 20116.8 cm

which rounds off to 20100 cm or 2.01 X 10^4 cm

Answer 3

Hmm...

1yrd = 0.9144m (looked that up)
0.9144m = 91.44cm (conversion for metres to cm = x100)

Therefore 220yrds = 220 x 91.44 = 20116.8cm or 2.01 x 10^4cm to 2.s.f.

All I can advise is practice, the more you do, the more conversion factors you will remember. Start with a 1 to something ratio and then scale up as needed.