Slide 8 - 1Copyright © 2009 Pearson Education, Inc.

WHAT YOU WILL LEARN

• The advantages of using the metric system• The basic units used in the metric system• Conversions within the metric system• Determining length, area, volume, mass, and

temperature in the metric system• Dimensional analysis and converting to and from

the metric system

Slide 8 - 2Copyright © 2009 Pearson Education, Inc.

Basic Terms – middle page 176

a little more than a quart

volumeLliter

about 2.2 pounds

masskgkilogram

a little more than a yard

lengthmmeter

Comparison to Customary

Common Use

AbbrevMetric Term

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Metric Prefixes

1/1000 of base unitmmilli1/100 of base unitccenti1/10 of base unitddeci

base unit10 base unitdadeka

100 base unithhecto1000 base unitkkilo

MeaningSymbolPrefix

Slide 8 - 4Copyright © 2009 Pearson Education, Inc.

A helpful way Changing Units within the Metric System King Henry Died By Drinking Chocolate Milk

In Kentucky students are taught Kentucky Has Deep And Dirty Coal Mines.

Do you know of another acronym for this? If so, share it on the Discussion Board this week.

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Example: Changing Units

Convert 54.6 m to km.

Slide 8 - 6Copyright © 2009 Pearson Education, Inc.

Example: Changing Units

Convert 54.6 m to km.

Solution: Meters is a smaller unit than km. Move the

decimal 3 places to the left, 0.0546 km.

Slide 8 - 7Copyright © 2009 Pearson Education, Inc.

Example: Changing Units

Convert 0.89 kg to cg.

Slide 8 - 8Copyright © 2009 Pearson Education, Inc.

Example: Changing Units

Convert 0.89 kg to cg.

Solution: Kilogram is a larger unit than centigram. Move

the decimal point 5 places to the right 0.89 kg = 89,000 cg

Slide 8 - 9Copyright © 2009 Pearson Education, Inc.

Example: Application - pay attention to all 3 steps needed to solve here.

A case of fruit juice contains twenty-four 0.75 liter bottles. How many 250 milliliter glasses can you fill using one case of juice?

Solution: The case of juice contains

24(0.75) = 18 L.

Converting 18 L = 18,000 mL. If each glass hold 250 mL,

then 18000mL / 250mL = 72 glasses can be filled.

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If one package sports drink mix makes 480 ml , how many ml of sports drink mix does 5 packages make?

a. 2400 ml

b. 24,000 ml

c. 2320 ml

d. 2900 ml

Slide 8 - 11Copyright © 2009 Pearson Education, Inc.

If one package sports drink mix makes 480 ml , how many ml of sports drink mix does 5 packages make?

a. 2400 ml

b. 24,000 ml

c. 2320 ml

d. 2900 ml

Slide 8 - 12Copyright © 2009 Pearson Education, Inc.

Length

The meter is used to measure things that we normally measure in yards and feet. A meter is a little more than a yard.

Centimeters and millimeters are used to measure what we normally measure in inches. A centimeter is a little less than a half of an

inch. A millimeter is about the thickness of a dime. .

Slide 8 - 13Copyright © 2009 Pearson Education, Inc.

Area

Areas are always expressed in square units.

Example:

The length of a rectangular park is 82.5 m, and its width is 25.4 m. Find the area of the park.

Solution: Area = length width.

A = 82.5 25.4

A = 2095.5 m2

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Volume – p188 table 5-3 When a figure has three dimensions; length, width

and height, the volume can be found. Volume can be expressed in terms of liters or cubic

meters. The abbreviation cc is often used instead of cm3 to

represent cubic centimeters. 1cm3= 1cc = 1mL (usually in liquids).

1 m3 = 1 kL

1 dm3 = 1 L

1 cm3 = 1 mL

Volume in LitersVolume in Cubic Units

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Volume

Example: An asthma patient must mix 0.25 cc of a bronchodilator with 2 cc of saline to use in an aerosol machine.

What is the total volume of drug and saline solution in milliliters? Hint: use this important relationship…1 cm3 = 1cc = 1 mL

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Volume

Example: An asthma patient must mix 0.25 cc of a bronchodilator with 2 cc of saline to use in an aerosol machine.

What is the total volume of drug and saline solution in milliliters?

Solution: 1 cm3 = 1cc = 1 mL The total volume is 0.25 + 2 or 2.25 cc, which

is equal to 2.25 mL.

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Mass

Although weight and mass are not the same, on Earth they are proportional to each other.

Mass is a measure of the amount of matter in an object.

Weight is the measure of gravitational pull on an object.

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Metric System

The kilogram is the basic unit of mass in the metric system. Example: A man has the mass of about 75 kg.

The gram is relatively small and used in place of the ounce. Example: A nickel has the mass of about 5 g.

The milligram is used in the medical and scientific fields for very small amounts.

Slide 8 - 19Copyright © 2009 Pearson Education, Inc.

Volume and Mass of Water – page 198 table 5-4

Volume in Cubic Units

1 m3 = 1 kL = 1 t (1000 kg)

1 dm3 = 1 L = 1 kg

1 cm3 = 1 mL = 1 g

Mass of WaterVolume in Liters

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Example: Capacity – another multistep problem

A fish tank is 1 m long, 60 cm high and 260 mm wide. Determine the number of liters that the tank holds. First,

convert all to meters 60 cm = ? m 260 mm = ? m Then, compute Volume in m3 (= m x m x m)

V l w h

10.26 0.6

0.156 m3

Slide 8 - 21Copyright © 2009 Pearson Education, Inc.

Example: Capacity

A fish tank is 1 m long, 60 cm high and 260 mm wide.

Determine the number of liters that the tank holds.

Since 1m3 = 1kL, we have V = .156 kL And converting to L, we get V = 156L.

V l w h

10.26 0.6

0.156 m3

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Example: Capacity

A fish tank is 1 m long, 60 cm high and 260 mm wide.

What is the mass of the water in kilograms.

Recall (page 198 table 5-4) that 1 L = 1kg

Since V = 156L that means V = 156kg

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Dimensional Analysis

Dimensional analysis is a procedure used to convert from one unit of measurement to a different unit of measurement.

A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1.

Examples of unit fractions:

16 oz

1 lb

1 hr

60 min

12 in.

1 ft

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U.S. Customary Units – see page 205 for lots of tables

1 pint = 2 cups 1 year = 365 days

1 cup (liquid) = 8 fluid ounces

1 day = 24 hours1 ton = 2000 pounds

1 hour = 60 minutes1 pound = 16 ounces

1 minute = 60 seconds1 mile = 5280 feet

1 gallon = 4 quarts1 yard = 3 feet

1 quart = 2 pints1 foot = 12 inches

U.S. Customary Units

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Example: Using Dimensional Analysis – You try

A recipe calls for 8 cups of blueberries. How many pints is this?Hint: look on your table to find a unit fraction that relates cups and

pints.Now,

8 cups times ( put in the unit fraction here so that the units will cancel out when multiplied)

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Example: Using Dimensional Analysis

A recipe calls for 8 cups of blueberries. How many pints is this?

Solution:

8 cups = 8 cups 1 pint

2 cups

4 pint s

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Example: Using Dimensional Analysis - you may need more than one unit fraction to get to your answer. Also “per” means divide.

Convert 75 miles per hour to inches per minute. (75 miles / 1 hour) Look on your table to find a unit fraction that relates miles

and some smaller unit (eventually you need inches).

Ideas??

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Example: Using Dimensional Analysis

Convert 75 miles per hour to inches per minute.Solution:

75mi

hr 75

mi

hr

5280ft

1 mi

12 in

1 ft

1 hr

60 min

75 5280 12

60

in

min = 79,200

in

min

Slide 8 - 29Copyright © 2009 Pearson Education, Inc.

Conversion to and from the Metric System – Volume – page 207

VOLUME

U.S. to Metric

1 quart (qt) ≈ 0.95 liter (l)

1 gallon (gal) ≈ 3.8 liters (l)

1 cubic foot (ft3) ≈ 0.03 cubic meter (m3)

1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)

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Example: Volume and Area

A gas tank holds 22.6 gallons of gas. How many liters is this? Look on your table to find a unit fraction that relates gallons and liters.

Ideas??

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Example: Volume and Area

A gas tank holds 22.6 gallons of gas. How many liters is this?

Since we need to get “gal” to cancel set up so it does.Solution:

3.8 l

22.6 gal = 85.88 lgal

Slide 8 - 32Copyright © 2009 Pearson Education, Inc.

Conversion to and from the Metric System – Length page 207

LENGTH

U.S. to Metric

1 inch (in.) ≈ 2.54 centimeters (cm)

1 foot (ft) ≈ 30 centimeters (cm)

1 yard (yd) ≈ 0.9 meter (m)

1 mile (mi) ≈ 1.6 kilometers (km)

Slide 8 - 33Copyright © 2009 Pearson Education, Inc.

Example: Converting Speed

A road in Toronto, Canada shows that the speed limit is 62 kph (kilometers per hour). Determine the speed in miles per hour. Here we go….

Find the appropriate unit fraction(s), recall per means divide, and put km on the bottom so it cancels out and leaves mi on top.

Slide 8 - 34Copyright © 2009 Pearson Education, Inc.

Example: Converting Speed – did you get this?

A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour.

Solution:

Since 62 km equals 38.75 mi, 62 kph is equivalent to 38.75 mph.

62 km

1 mi

1.6 km

62

1.6mi 38.75 mi

Slide 8 - 35Copyright © 2009 Pearson Education, Inc.

Conversions

To covert from Celsius to Fahrenheit use the following formula.

To covert from Fahrenheit to Celsius use the following formula.

F

9

5C 32

C

5

9F 32

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Example: Conversions

The air temperature on a warm summer day is about 85ºF. What is the equivalent temperature on the Celsius thermometer? Solution:

C 5

9F 32

C 5

985 32

C 5

953

C 29.4

The equivalent temperature is about 29.4ºC.

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Change 95º C to degrees Fahrenheit

a. 35º F

b. 70.56º F

c. 228.6º F

d.203º F

F

9

5C 32

Slide 8 - 38Copyright © 2009 Pearson Education, Inc.

Change 95º C to degrees Fahrenheit

a. 35º F

b. 70.56º F

c. 228.6º F

d.203º F