In general, you use conversion factors to convert from one unit to another.
They come from relations that you know or can look up. Some examples are
- 3 ft = 1 yd
- 1 ft = 12 in
- 1 in = 2.54 cm
- 1 lb = 454 g
From them, you create conversion factors like "3 ft"/"1 yd"3 ft1 yd and "1 yd"/"3 ft"1 yd3 ft.
In a given calculation, you choose the conversion factor that makes the units cancel and gives you the correct units for your answer.
Yards to centimetres
You have to do a number of conversions:
"yards → feet → inches → centimetres"yards → feet → inches → centimetres
1.23 color(red)(cancel(color(black)("yd"))) × "3 ft"/(1color(red)(cancel(color(black)(" yd")))) = "3.69 ft"
3.69 color(red)(cancel(color(black)("ft"))) × "12 in"/(1color(red)(cancel(color(black)(" ft")))) = "44.28 in"
44.28 color(red)(cancel(color(black)("in"))) × "2.54 cm"/(1 color(red)(cancel(color(black)("in")))) = "112 cm"
You could also have done the calculation in one step:
1.23 color(red)(cancel(color(black)("yd"))) × (3 color(red)(cancel(color(black)("ft"))))/(1 color(red)(cancel(color(black)("yd")))) × (12 color(red)(cancel(color(black)("in"))))/(1 color(red)(cancel(color(black)("ft")))) × "2.54 cm"/(1 color(red)(cancel(color(black)("in")))) = "112 cm"
Pounds to grams
1.23 color(red)(cancel(color(black)("lb"))) × "454 g"/(1 color(red)(cancel(color(black)("lb")))) = "558 g"
Notice that in every case we chose the conversion factor to make the units cancel.
