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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
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5.1
Basic Terms and Conversions within the Metric System
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SI System and U.S. Customary System
U.S customary system
Systéme international d’unités or SI system.
referred to as the metric system
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Advantages to Using the Metric System
Accepted worldwide standard measurement
Only one unit of measurement
Based on the number 10
Less need for fractions
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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
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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
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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
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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.
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Example: Changing Units
Convert 15 L to mL.
Hint. There are 1000 mL in one Liter.
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Example: Changing Units
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.
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Example: Changing Units
Convert 0.89 kg to cg.
Hint. There are 100 centigrams in one gram, and 1000 grams in one kilogram.
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Example: Changing Units
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
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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
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5.2
Length, Area, and Volume
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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.
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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
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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
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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?
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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.
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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
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5.3
Mass and Temperature
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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.
The metric tonne (t) is used to express mass of heavy items. One metric tonne = 1000 kg.
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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
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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
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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.
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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
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Temperature
The term degrees Celsius (ºC) is used to measure temperature.
Water boils212ºF100ºC
Body temperature98.6ºF37ºC
Comfortable room71.6ºF22ºC
Water freezes32ºF0ºC
DescriptionºFºC
Temperature
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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
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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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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
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5.4
Dimensional Analysis and Conversions to and from the
Metric System
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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
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
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
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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)
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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)
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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)
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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)
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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)
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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
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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
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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