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Copyright © 2005 Pearson Education, Inc.

Chapter 8

The Metric System


8.1

Basic Terms and Conversions within the Metric System

4Copyright © 2005 Pearson Education, Inc.

SI System and U.S. Customary System

Most countries of the world use the SI system The SI system is referred to as the metric system in the United States.Two systems of weights and measures exist side by side in the United States today, U.S customary system and the metric system.


Advantages to Using the Metric System

The metric system is the worldwide accepted standard measurement system.There is only one unit of measurement for each physical quantity.The SI system is based on the number 10, allowing less need for fractions.


Basic Terms

a little more than a quart

volumeLliter

about 2.2 pounds

masskgkilogram

a little more than a yard.

lengthmmeter

Comparison to Customary

Common UseAbbrev.Metric Term


Metric Prefixes

of base unitmmilli

of base unitccenti

of base unitddeci

base unit

10 base unitdadeka

100 base unithhecto

1000 base unitkkilo

MeaningSymbolPrefix

×

×

×

110

11001

1000


Changing Units within the Metric System

To change from a smaller unit to a larger unit move the decimal point in the original quantity one place to the left for each larger unit of measure until you obtain the desired unit of measure.To change from a larger unit to a smaller unit, move the decimal point in the original quantity one place to the right for each smaller unit of measurement until you obtain the desired unit of measure.


Example: Changing Units

Convert 54.6 m to km.Convert 15 L to mL.Convert 0.89 kg to cg.

Solutions:Meters is a smaller unit than km. Move the decimal 3 places to the left, 0.0546.Liter is a larger unit than milliliter. Move the decimal point 3 places to the right, 15,000.0.89 kg = 89,000 cg


Example: Application

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 glasses can be filled.18,000 72

250=


8.2

Length, Area, and Volume


Length

The meter is used to measure things that we normally measure in yards and feet. 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.

Example: The length of a pair of scissors would be measured in centimeters.


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. ×

2

82.5 25.42095.5 m

AA= ×

=


Volume

When a figure has three dimensions; length, width and height, the volume can be found.The volume of an item can be considered the space occupied by the item.Volume can be expressed in terms of liters or cubic meters.

1 m3 = 1 kL

1 dm3 = 1 L

1 cm3 = 1 mL

Volume in LitersVolume in Cubic Units


Volume

When the volume of a liquid is measured, the abbreviation cc is often used instead of cm3 to represent cubic centimeters.

Example: An asthma patient must mix 0.25 cc of a bronchodilator with 2 cc of saline to use in an aerosol machine.How many milliliters of the bronchodilator will be administered?What is the total volume of drug and saline solution in milliliters?


Volume continued

Solution: Since 1 cc is equal in volume to 1 milliliter, there will be 0.25 milliliters of the bronchodilator.The total volume is 0.25 + 2 or 2.25 cc, which is equal to 2.25 mL.


Example: Volume Application

A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters?

Solution:

( )

2

2

3

3.14 3 12

339.12 cm339.12 mL

V r h

V

VV

π=

=

==


8.3

Mass and Temperature


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.


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.The metric tonne is used to express mass of heavy items. One metric tonne = 1000 kg.


Example: Choosing an Appropriate Unit

Determine which metric unit you would use to express the mass of the following.

a) A spider c) A bicycleb) A nickel d) A nickel

Solution:a) Milligrams c) Kilogramsb) Grams d) Grams


Volume and Mass of Water

Volume in Cubic Units

1 m3 = 1 kL = 1 t (1000 kg)1 dm3 = 1 L = 1 kg1 cm3 = 1 mL = 1 g

Mass of WaterVolume in Liters


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.What is the mass of the water in kilograms.


Example: Capacity continued

Solution:

Since 1 m3 of water = 1 kL of water,0.156 m3 = 0.156 kL, or 156 liters of water

Since 1L = 1 kg, 156 L = 156 kg of water.

3

1 0.26 0.60.156 m

V l w h= × ×= × ×

=


Temperature

The term degrees Celsius is used to measure temperature.

( )Co

Water boils212100

Body temperature98.637

Comfortable room71.622

Water freezes320

Description

Temperature

Co Fo

Co

Co

Co

Co Fo

Fo

Fo

Fo


Example: Choose or

The temperature of a can of frozen juice about 2 __.The temperature of a person with a fever is about 101.5 __.The temperature of a bowl of hot soup is about 175 __.

Solution: a) b) c)

Fo .Co

.Co Fo Fo


Conversions

To covert from Celsius to Fahrenheit use the following formula.

To covert from Fahrenheit to Celsius use the following formula.

9F C 325

= + ( )5C F 329

= −


Example: Conversions

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

Solution:

The equivalent temperature is about 29.4

( )

( )

( )

5C F 3295C 85 3295C 53929.4C

= −

= −

=

≈

.Co

Fo


Example: Conversions

The temperature of a cold glass of milk is about 5 . What is the equivalent temperature on the Fahrenheit thermometer?

Solution:

The equivalent temperature is about 41

Co

( )

9F C 3259F 5 325

F 9 32F 41

= +

= +

= +=

.Fo


8.4

Dimensional Analysis and Conversions to and from the

Metric System


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 hr 12 in. 1 lb 60 min 1 ft


U.S. Customary Units

1 pint = 2 cups

1 year = 365 days1 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


Example: Using Dimensional Analysis

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

Solution:

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

( ) 1 pint8 cups = 8 cups 4 pint s2 cups

⎛ ⎞=⎜ ⎟

⎝ ⎠

( )( )( )75 5280 12mi mi 5280ft 12 in 1 hr in75 75hr hr 1 mi 1 ft 60 min 60 min

in = 79,200min

⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞= =⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠


Conversion to and from the Metric System


Example: Volume and Area

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

Solution:

The area of a box is 14.25 in2. What is its area in square centimeters?

Solution:

3.8 L22.6 gal = 85.88 Lgal

=

22 2

2

6.5 cm14.25 in 92.625 cm1 in

⎛ ⎞=⎜ ⎟

⎝ ⎠


Example: Converting Speed

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 kpm is equivalent to 38.75 mph.

1 mi 6262 km mi 38.75 mi1.6 km 1.6⎛ ⎞ = =⎜ ⎟⎝ ⎠


Example: Weight (Mass) Conversion for Medication

A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given?.

Solution:

The dosage of the medication is 73.92 mg.

16 oz8 lbs 128 oz 4 oz 132 oz1 lb 28 g 1 kg 20 mg132 oz 3.696 kg 73.92 mgoz 1000 g 1 kg

⎛ ⎞ = + =⎜ ⎟⎝ ⎠

⎛ ⎞ ⎛ ⎞⎛ ⎞ = =⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

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