1. First write down the desired quantity
Unit Conversions
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
First write down the desired quantity

2. Next, equate desired quantity to the given quantity
Factor label example
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
Next, equate desired quantity to the given quantity

3. Now we have to choose a conversion factor
Factor label example
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
Now we have to choose a conversion factor

4. What conversion factors are possible?
Factor label example
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
1 km
0.621 mi
0.621 mi
1 km
What conversion factors are possible?

5. Pick the one that will allow you to cancel out miles
Factor label example
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

6. Pick the one that will allow you to cancel out miles
Factor label example
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

7. Cross out common factors
Factor label example
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621 mi
# km
= 47 mi
Cross out common factors

8. Factor label example Now finish the math.
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
= 75.7 km
# km
= 47
Now finish the math.

9. Factor label example The final answer is 75.7 km
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
= 75.7 km
# km
= 47
The final answer is 75.7 km

10. Summary The previous problem was not that hard
In other words, you probably could have done it faster using a different method
However, for harder problems the factor label method is easiest

11. More examples
You want to buy 100 U.S. dollars. If the exchange rate is 1 Can$ = 0.65 US$, how much will it cost?
# Can$
= 100 US$
x 1 Can$
0.65 US$
= Can$

12. There are 12 inches in a foot, 0
There are 12 inches in a foot, inches in a centimeter, and 3 feet in a yard. How many cm are in one yard?
# cm
= 1 yd
x 3 ft
1 yd
x 12 in
1 ft
x 1 cm
0.394 in
= cm