1. Objective A: Convert from one American unit of length to another.
Here in the United States, we are used to American Units of length; inches, feet, yards, miles.
At times, it may be necessary to write a given length in different units.
Example: 1 foot = 12 inches
Below is a list of common equivalents.
American Units of Length (conversions)
12 inches (in.) = 1 foot (ft)
3 feet = 1 yard (yd)
36 inches = 1 yard
5280 feet = 1 mile (mi)
We can use these conversion factors to convert from one unit to another.
Recall: Any number divided by itself equals 1.
Therefore: ,
etc.
Procedure: To convert from one unit to another unit
Multiply a given quantity by a conversion factor with the given units in the denominator and the desired units in the numerator. It may take more than one conversion factor to get to the desired units.
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2. Example 1. Complete: 48 in = _____ ft
Solution:
1. Write down the conversion factor:
2. Multiply the given by a conversion factor with the same units in the denominator.
The like units reduce. Then simply the fractions.
Your Turn Problem #1
Complete: 60 in = _____ ft
Answer: 5 ft

3. Example 2. Complete: 22 ft = _____ yd
Solution:
1. Write down the conversion factor:
2. Multiply the given by a conversion factor with the same units in the denominator.
The like units reduce. Then simply the fractions.
Your Turn Problem #2
Complete: 35 ft = _____ yd

4. Example 3. Complete: 5 yd = _____ in
Solution:
1. Write down the conversion factor(s):
2. We Will need to use two conversion factors to convert to the desired units.
The like units reduce. Then simply the fractions.
Your Turn Problem #3
Complete: 7 yd = _____ in

5. Solution:
1. Write down the conversion factor(s):
2. Multiply the given by a conversion factor with the same units in the denominator.
The like units reduce. Then simply the fractions.
Your Turn Problem #4

6. Objective B: Metric Units of Length
The metric system is used by most of the world, and the United States is now making greater use of it as well. Because it is based on powers of 10, the metric system allows for easy conversion between smaller and larger units.
The basic unit of length is the meter. It is just over 1 yard.
We can convert units by using conversion factors just as we did with American units. However, there is a much easier method to converting units.
Example: Complete: 3 km = ______ m
Solution:
How about a shortcut? We can see be the answers, it’s still the basic number, but the decimal place has moved either to the left or right.
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Example: Complete: 7 m = ______ km
Solution:

7. Converting from one unit to another can be done by moving the decimal point the correct number of places to the right or left. We will use the chart below to determine which direction and the number of places to move the decimal point.
Example: If we want to change from km to m, count the steps from km to m.
Answer: 3 places to the right.
Example: If we want to change from cm to hm, count the steps from cm to hm.
Answer: 4 places to the left.

8. Example 5a: Complete: 7250 m = ______ km
Solution:
Count from m to km.
Answer: 3 places to the left. Therefore move the decimal in the given problem 3 places to the left.
7250 m =7.250 km or 7.25 km
Example 5b: Complete: 8.4 cm = ______ m
Solution:
Count from cm to m.
Answer: 2 places to the left. Therefore move the decimal in the given problem 2 places to the left.
8.4 cm =0.084 m
Your Turn Problem #5

9. Objective C: Converting Length between of Systems
There are times when we wish to convert from one system to another.
We can make conversions between American and metric units by using the following table.
American
Metric
1 in.
2.540 cm
1 ft
0.305 m
1 yd
0.914 m
0.621 mi
1 km
1.094 yd
1 m
3.281 ft
in.
Don’t worry, you don’t need to memorize this table. There is usually more than one method from converting from one system to another. Another issue is the decimals. Without a calculator, these problems can be pretty tedious.
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10. Example 6. Complete: 12 cm = ______ in
American
Metric
1 in.
2.540 cm
1 ft
0.305 m
1 yd
0.914 m
0.621 mi
1 km
1.094 yd
1 m
3.281 ft
in.
Example 6. Complete: 12 cm = ______ in
Solution:
1. Write down the conversion factor:
2. Multiply the given by a conversion factor with the same
units in the denominator.
Your Turn Problem #6
Complete: 12 ft = _____ m

11. Objective D: Convert from one American unit of weight to another.
American Units of Weight
1 pounds (lb) = 16 ounces (oz)
1 ton (t) = 2000 pounds (lb)
Example 7. Complete: 3 ¼ lb = _____ oz
Solution:
1. Write down the conversion factor:
2. Multiply the given by a conversion factor with the same units in the denominator.
Your Turn Problem #7
Complete: ¾ t = _____ lb
Answer: 1500 lb

12. Objective E: Metric Units of Weight
The basic unit of weight in the metric system is the gram (g).
Examples: A large paper clip weighs approx. 1g. The weight of a penny is 2.5 g.
We will still use the same shortcut for moving the decimal point. The unit is just different.
Example 8: Complete: 530 g = ______ kg
Solution:
Count from g to kg.
Answer: 3 places to the left. Therefore move the decimal in the given problem 3 places to the left.
530 g = kg or 0.53 kg
Your Turn Problem #8

13. Another unit commonly used in the medical field is the microgram.
1,000,000 mcg = 1 g or
Placing mcg on our conversion chart gives:
Example 9: Complete: mg = ______ mcg
Solution:
Count from mg to mcg.
Answer: 3 places to the right. Therefore move the decimal in the given problem 3 places to the right.
0.02 mg = 20 mcg
Your Turn Problem #9
Complete: mg = _____ mcg

14. Objective F: Converting Weight between of Systems
There are times when we wish to convert from one system to another.
We can make conversions between American and metric units by using the following table.
American
Metric
1 lb
0.45 kg
1 oz
28.35 g
0.04 oz
1 g
2.2 lb
1 kg
Example 10. Complete: lb = ______ kg
Solution:
1. Write down the conversion factors.
We have two choices. Make sure lb’s are on the bottom of the fraction.
Note: These conversions are approximations, not exact numbers.
2. Since it is easier to multiply than divide, let’s use the 1st conversion.
If we use the 2nd conversion:
Notice, the answers are not the same. Again, these conversions are not exact, they’re rounded.
Your Turn Problem #10
Complete: 85 kg = _____ lb

15. Objective G: Convert from one American unit of capacity to another.
American Units of Capacity
1 gallon (gal) = 4 quarts (qt)
1 pt = 2 cups = 16 ounces (oz)
1 qt = 2 pints (pt)
1 cup = 8 oz
Example 11. Complete: 7 qt = _____ gal
Solution:
1. Write down the conversion factor:
2. Multiply the given by a conversion factor with the same units in the denominator.
Your Turn Problem #11
Complete: 36 oz = _____ cups
Answer: 4 ½ cups

16. Example 12. Complete: 3 gal = _____ cups
American Units of Capacity
Solution:
1. Multiply the given by conversion factors with the same units in the denominator to get to the desired units.
1 gallon (gal) = 4 quarts (qt)
1 pt = 2 cups = 16 ounces (oz)
1 qt = 2 pints (pt)
1 cup = 8 oz
Your Turn Problem #12
Complete: 2 ½ gal = _____ cups
Answer: 40 cups

17. Objective H: Metric Units of Capacity
The basic unit of capacity in the metric system is the liter (L).
Examples: Soda bottles typically come in 2 liter bottles.
We will still use the same shortcut for moving the decimal point. The unit is just different.
Example 13: Complete: ml = _____ L
Solution:
Count from ml to L.
Answer: 3 places to the left. Therefore move the decimal in the given problem 3 places to the left.
4000 ml = L or 4 L
Your Turn Problem #13

18. Objective I: Converting Capacity between of Systems
American
Metric
1 gal
3.79 L
1 qt
0.95 L
1 fl oz
29.6 ml
1.06 qt
1 L
0.26 gal
Please note: these conversions are all approximations.
Example 14. Complete: 2 L = ______ gal
Solution:
1. Write down the conversion factors.
We have two choices. Make sure L’s are on the bottom of the fraction.
2. Since it is easier to multiply than divide, let’s use the 1st conversion.
Your Turn Problem #14
Complete: 8 fl oz = _____ ml
Answer: ml
The End