Copyright © 2009 Pearson Education, Inc. Welcome to MM150! Unit 5 Seminar To resize your pods:...

Copyright © 2009 Pearson Education, Inc.

Welcome to MM150!

Unit 5 Seminar

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MM150 Unit 5 Seminar Agenda

• Metric System

• Length, Area, and Volume

• Mass and Temperature

• Conversion to and from the Metric System


5.1

Basic Terms and Conversions within the Metric System


SI System and U.S. Customary System

U.S customary system

Systéme international d’unités or SI system.

referred to as the metric system


Advantages to Using the Metric System

Accepted worldwide standard measurement

Only one unit of measurement

Based on the number 10

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 base unitdadeka

100 base unithhecto1000 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


Example: Changing Units

Convert 54.6 m to km.

Solution: Meters is a smaller unit than km. There are 1000 m in one km. Divide 54.6m/1000 or … Move the decimal 3 places to the left, 0.0546

km.



Convert 15 L to mL.

Hint. There are 1000 mL in one Liter.



Convert 15 L to mL.

Solution: Liter is a larger unit than milliliter. There are 1000 mL in one L. Multiply 15L * 1000 or … Move the decimal point 3 places to the right,

15,000 mL.



Convert 0.89 kg to cg.

Hint. There are 100 centigrams in one gram, and 1000 grams in one kilogram.



Convert 0.89 kg to cg.

Solutions: Kilogram is a larger unit than centigram. There are 100 centigrams in one gram, and

1000 grams in one kilogram. Multiply 0.89 kg * 100,000 or … 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 hold 250 mL,

then glasses can be filled.

18,000

250= 72


5.2

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 8m, and its width is 2m. Find the area of the park.

Solution: Area = length width.

A = 8m x 2m

A = 16m2


Volume

When a figure has three dimensions; length, width and height, the volume can be found.

The volume of an item is how much can be held 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

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

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: V = (Area base)h

V = πr2h

V = 3.14(3)212

V = 339.12 cm3

V = 339.12 mL

6cm


5.3

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 (t) 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 bicycle

b) A nickel d) A box of cereal

Solution:

a) Milligrams c) Kilograms

b) 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 kg

1 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.

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


Example: Choose ºF or ºC

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) ºC b) ºF c) ºF


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


5.4

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 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

Copyright © 2009 Pearson Education, Inc. Welcome to MM150! Unit 5 Seminar To resize your pods:...

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