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"# and #"1 yd"/"3 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"#
#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.
