objective a: convert from one american unit of length to another

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7.1 Measurement Section 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

Recall: Any number divided by itself equals 1.

Therefore: 12 in 1 ft1

1 ft 12 in

3 ft 1 yd1

1 yd 3 ft , etc.,

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 yard5280 feet = 1 mile (mi)

We can use these conversion factors to convert from one unit to another.

Procedure: To convert from one unit to another unitMultiply 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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Example 1. Complete: 48 in = _____ ft

Solution: 1. Write down the conversion factor:12 in 1 ft

or 1 ft 12 in

2. Multiply the given by a conversion factor with the same units in the denominator.

48 in 1 ft1 12 in

The like units reduce. Then simply the fractions.

48 ft =

124 ft

Answer: 5 ft

Your Turn Problem #1

Complete: 60 in = _____ ft

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Example 2. Complete: 22 ft = _____ yd

Solution: 1. Write down the conversion factor:3 ft 1 yd

or 1 yd 3 ft


22 ft 1 yd

1 3 ftThe like units reduce. Then simply the fractions.

22 yd =

31

7 yd3


Complete: 35 ft = _____ yd2

Answer: 11 yd3

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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.

5 yd 3 ft 12 in

1 1 yd 1 ftThe like units reduce. Then simply the fractions. =180 in


Complete: 7 yd = _____ in

Answer: 252 ft

12 in 1 ft 3 ft 1 yd or and or

1 ft 12 in 1 yd 3 ft

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Solution: 1. Write down the conversion factor(s):


7 yd 3 ft

3 1 ydThe like units reduce. Then simply the fractions. =7 ft

Answer: 21 in

3 ft 1 yd or

1 yd 3 ft

1 Complete: 2 yd = E xample _____4.

3 ft


Complete: 1 ft = _____ in 4

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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.

1 kilometer (km) = 1000 meters (m)

1 hectometer (hm) = 100 meters (m)

1 dekameter (dam) = 10 meters (m)

1 met

Metric Units of Length

er (m) = 1 m

11 decimeter (dm)

= meter1

0

(m)

11 centimeter (cm) = meter (m)10011 millimeter (mm) = meter (m)1000

3 km 1000 m1 1 km

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: 3000 m

7 m 1 km1 1000 m

Example: Complete: 7 m = ______ km

Solution: 0.007 m

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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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.

km hm dam m dm cm mm

Example: If we want to change from km to m, count the steps from km to m.

Answer: 3 places to the right.

km hm dam m dm cm mm

Example: If we want to change from cm to hm, count the steps from cm to hm.

Answer: 4 places to the left.

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Example 5a: Complete: 7250 m = ______ km

Solution: km hm dam m dm cm mmCount 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: km hm dam m dm cm mmCount from cm to m.


8.4 cm =0.084 m

Answer:

a) 9.427 km

b) 0.0063 m

Your Turn Problem #5Complete the following:

a) 9427 m = _____ km

b) 6.3 mm = _______m

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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 1 m

39.370 in. 1 m

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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Objective C: Converting Length between of Systems

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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 1 m

39.370 in.

1 m

Example 6. Complete: 12 cm = ______ in

Solution: 1. Write down the conversion factor:


12 cm 1 in1 2.54 cm

12in2.54

4.72 in


Complete: 12 ft = _____ m

Answer: 3.66 m

1 in 2.54 cm or

2.54 cm 1 in

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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:1 lb 16 oz

or 16 oz 1 lb


13 lb 16 oz

4 1 lb =52 oz

Answer: 1500 lb


Complete: ¾ t = _____ lb

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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.

1 kilogram (kg) = 1000 gram (g)

1 hectogram (hg) = 100 gram (g)

1 dekagram (dag) = 10 gram (g)

1 gram (g) = 1

Metric Units of Weight

g

11 decigram (d

g) = gram (g)10

1

centigr 1am (cg) = gram (g)10011 milligram (mg) = gram (g)1000

We will still use the same shortcut for moving the decimal point. The unit is just different.

Example 8: Complete: 530 g = ______ kg

Solution:

kg hg dag g dg cg mg

Count from g to kg.


530 g = 0.530 kg or 0.53 kg

Answer:

a) 300 mg

b) 0.12 kg


a) 0.3 g = _____ mg

b) 120,000 mg = _______ kg

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Another unit commonly used in the medical field is the microgram.

1,000,000 mcg = 1 g or 1

g = 0.000001 g1,000,000

Placing mcg on our conversion chart gives:

kg hg dag g dg cg mg ___ ___ mcg

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

Answer:

9 mcg


Complete: 0.009 mg = _____ mcg

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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: 175 lb = ______ kg

Solution: 1. Write down the conversion factors.We have two choices. Make sure

lb’s are on the bottom of the fraction.

2. Since it is easier to multiply than divide, let’s use the 1st

conversion.

0.45 kg 1 kg or

1 lb 2.2 lb

175 lb 0.45 kg

1 1 lb78.8kg

Note: These conversions are approximations, not exact numbers.

If we use the 2nd conversion:

175 lb 1 kg

1 2.2 lb79.5 kg

Notice, the answers are not the same. Again, these conversions are not exact, they’re rounded.

Answer:

187 lb


Complete: 85 kg = _____ lb

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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:1 gal 4 qt

or 4 qt 1 gal


7 qt 1 gal1 4 qt

31 gal

4 =

Answer: 4 ½ cups


Complete: 36 oz = _____ cups

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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 12. Complete: 3 gal = _____ cups

Solution: 1. Multiply the given by conversion factors with the same units in the denominator to get to the desired units.

3 gal 4 qt 2 pt 2 cups

1 1 gal 1 qt 1 pt

48 = cups

Answer: 40 cups


Complete: 2 ½ gal = _____ cups

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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.

1 kiloliter (kl) = 1000 liter (L)

1 hectoliter (hl) = 100 liter (L)

1 dekaliter (dal) = 10 liter (L)

1 lit

Metric Units of Capacity

er (L) = 1 L

11 deciliter (dl)

= liter (10

L)

11 centiliter (cl) = liter (L)10011 milliliter (ml) = liter (L)1000

We will still use the same shortcut for moving the decimal point. The unit is just different.

Example 13: Complete: 4000 ml = _____ L

Solution:

kl hl dal L dl cl ml

Count from ml to L.


4000 ml = 4.000 L or 4 L

Answer:

a) 270 L

b) 5.75 dal


a) 0.27 kl = _____ L

b) 575 dl = _______ dal

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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 1 L

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.

0.26 gal 3.79 L or

1 L 1 gal

2 L 0.26 gal1 1 L

0.52 galYour Turn Problem #14

Complete: 8 fl oz = _____ ml

Answer: 236.8 mlThe End6-11-08

objective a: convert from one american unit of length to another

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