# Question 60ef7

Jan 24, 2016

$\text{1.23 yd = 112 cm}$ and $\text{1.23 lb = 558 g}$

#### Explanation:

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 $\text{3 ft"/"1 yd}$ and $\text{1 yd"/"3 ft}$.

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:

$\text{yards → feet → inches → centimetres}$

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.