Objective A: Convert from one American unit of length to another.

1. Below is a list of common equivalents. American Units of Length (conversions) We can use these conversion factors to convert from one unit to another. 12 inches (in.) = 1 foot (ft) 3 feet = 1 yard (yd) 36 inches = 1 yard 5280 feet = 1 mile (mi) 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. Next Slide 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

2. Example 1. Complete: 48 in = _____ ft Solution: Your Turn Problem #1 Complete: 60 in = _____ ft 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. Answer: 5 ft

3. Your Turn Problem #2 Complete: 35 ft = _____ yd 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.

4. Your Turn Problem #3 Complete: 7 yd = _____ in 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.

5. Your Turn Problem #4 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.

6. 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. Example: Complete: 7 m = ______ km Solution: Next Slide 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.

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. 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 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 Example 5a: Complete: 7250 m = ______ km Example 5b: Complete: 8.4 cm = ______ m Your Turn Problem #5 Solution: Solution:

9. 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. Next Slide 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.

10. Your Turn Problem #6 Complete: 12 ft = _____ m 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.

11. Your Turn Problem #7 Complete: ¾ t = _____ lb 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. Answer: 1500 lb

12. We will still use the same shortcut for moving the decimal point. The unit is just different. Example 8: Complete: 530 g = ______ kg Solution: Your Turn Problem #8 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. 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 = 0.530 kg or 0.53 kg

13. 1,000,000 mcg = 1 g or Your Turn Problem #9 Complete: 0.009 mg = _____ mcg Another unit commonly used in the medical field is the microgram. Placing mcg on our conversion chart gives: Example 9: Complete: 0.02 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

14. Example 10. Complete: 175 lb = ______ kg Solution: If we use the 2nd conversion: Your Turn Problem #10 Notice, the answers are not the same. Again, these conversions are not exact, they’re rounded. Complete: 85 kg = _____ lb 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. 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.

15. Your Turn Problem #11 Complete: 36 oz = _____ cups 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. Answer: 4 ½ cups

16. Your Turn Problem #12 Complete: 2 ½ gal = _____ cups Example 12. Complete: 3 gal = _____ cups 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 Solution: 1. Multiply the given by conversion factors with the same units in the denominator to get to the desired units. Answer: 40 cups

17. We will still use the same shortcut for moving the decimal point. The unit is just different. Example 13: Complete: 4000 ml = _____ L Solution: Answer: 3 places to the left. Therefore move the decimal in the given problem 3 places to the left. 4000 ml = 4.000 L or 4 L Your Turn Problem #13 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. Count from ml to L.

18. Example 14. Complete: 2 L = ______ gal Solution: Your Turn Problem #14 Complete: 8 fl oz = _____ ml Answer: 236.8 ml The End 6-11-08 Objective I: Converting Capacity between of Systems Please note: these conversions are all approximations. 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.