Slide 8 - 1 Copyright © 2009 Pearson Education, Inc. Unit 5 The Metric System.

1Copyright © 2009 Pearson Education, Inc.

Unit 5The Metric System


SI System and U.S. Customary System

Most countries of the world use the Systéme international d’unités or SI system, 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.

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 Use

AbbrevMetric Term


Metric Prefixes

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

base unit10 x base unitdadeka

100 x base unithhecto1000 x base unitkkilo

MeaningSymbolPrefix


Changing Units within the Metric System

Measure of length

kilometer hectometer dekameter

Symbol km hm dam

Number of meters

1000 m 100 m 10 m

Measure of length

meter decimeter centimeter millimeter

Symbol m dm cm mm

Number of meters

1 m 0.1 m 0.01 m 0.001 m


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 km. Liter is a larger unit than milliliter. Move the

decimal point 3 places to the right, 15,000 mL. Kilogram is a larger unit than centigram. Move

the decimal point 5 places to the right 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 holds 250 mL, then 72 glasses can be filled.

18,000

250= 72


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 x width.

A = 82.5 25.4

A = 2095.5 m2


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. When the volume of a liquid is measured, the abbreviation cc

is often used instead of cm3 to represent cubic centimeters.

1 m3 = 1 kL

1 dm3 = 1 L

1 cm3 = 1 mL

Volume in LitersVolume in Cubic Units


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:

V r 2h

V 3.14 3 2 12

V 339.12 cm3

V 339.12 mL


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 (t) is used to express mass of heavy items. One metric tonne = 1000 kg.


Volume and Mass of Water

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


Example: CapacityA 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.

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.

V l w h

10.26 0.6

0.156 m3


Temperature

The term degrees Celsius (ºC) is used to measure temperature.

Water boils212ºF100ºC

Body temperature98.6ºF37ºC

Comfortable room71.6ºF22ºC

Water freezes32ºF0ºC

DescriptionºFºC

Temperature


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


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.


Example: Conversions

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

Solution:

The equivalent temperature is about 41ºF.

F 9

5C 32

F 9

55 32

F 9 32

F 41


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


U.S. Customary Units

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


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:

8 cups = 8 cups 1 pint

2 cups

4 pint s

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


Conversion to and from the Metric System - Length

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)


Conversion to and from the Metric System - Area

AREA

U.S. to Metric

1 square inch (in.2) ≈ 6.5 square centimeters (cm2)

1 square foot (ft2) ≈ 0.09 square meter (m2)

1 square yard (yd2) ≈ 0.8 square meter (m2)

1 square mile (mi2) ≈ 2.6 square kilometers (km2)

1 acre ≈ 0.4 hectare (ha)


Conversion to and from the Metric System - Volume

VOLUME

U.S. to Metric

1 teaspoon (tsp) ≈ 5 milliliters (ml)

1 tablespoon (tbsp) ≈ 15 milliliters (ml)

1 fluid ounce (fl oz) ≈ 30 milliliters (ml)

1 cup (c) ≈ 0.24 liter (l)

1 pint (pt) ≈ 0.47 liter (l)


Conversion to and from the Metric System - Volume

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)


Conversion to and from the Metric System - Weight (Mass)

WEIGHT OR MASS

U.S. to Metric

1 ounce (oz) ≈ 28 grams (g)

1 pound (lb) ≈ 0.45 kilogram (kg)

1 ton (T) ≈ 0.9 tonne (t)


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 l

22.6 gal = 85.88 lgal

14.25 in2 6.5 cm2

1 in2

92.625 cm2


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 kph is equivalent to 38.75 mph.

62 km

1 mi

1.6 km

62

1.6mi 38.75 mi


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.

8 lbs 16 oz

1 lb

4 oz 128 oz 4 oz 132 oz

132 oz28 g

oz

1 kg

1000 g

20 mg

1 kg

73.92 mg

Slide 8 - 1 Copyright © 2009 Pearson Education, Inc. Unit 5 The Metric System.

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