1. SEVENTH EDITION and EXPANDED SEVENTH EDITION

2. Chapter 8
The Metric System

3. Basic Terms and Conversions within the Metric System
8.1
Basic Terms and Conversions within the Metric System

4. 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.

5. 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.

6. Basic Terms a little more than a quart volume L liter about 2.2 pounds
mass kg
kilogram
a little more than a yard.
length m
meter
Comparison to Customary
Common Use
Abbrev.
Metric
Term

7. Metric Prefixes of base unit m milli c centi d deci base unitda
deka
100 base unit h
hecto
base unit k
kilo
Meaning
Symbol
Prefix

8. 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.

9. 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,
Liter is a larger unit than milliliter. Move the decimal point 3 places to the right, 15,000.
0.89 kg = 89,000 cg

10. 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.

11. 8.2
Length, Area, and Volume

12. 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.

13. 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.

14. 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 m = kL
1 dm = L
1 cm = mL
Volume in Liters
Volume in Cubic Units

15. 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?

16. 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 or 2.25 cc, which is equal to 2.25 mL.

17. 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:

18. 8.3
Mass and Temperature

19. 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.

20. 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.

21. 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 nickel
Solution:
a) Milligrams c) Kilograms
b) Grams d) Grams

22. Volume and Mass of Water
Volume in Cubic Units
1 m = kL = t (1000 kg)
1 dm = L = kg
1 cm = mL = g
Mass of Water
Volume in Liters

23. 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.

24. Example: Capacity continued
Solution:
Since 1 m3 of water = 1 kL of water,
0.156 m3 = kL, or 156 liters of water
Since 1L = 1 kg, 156 L = 156 kg of water.

25. Temperature The term degrees Celsius is used to measure temperature.
Water boils
212
100
Body temperature
98.6 37
Comfortable room
71.6 22
Water freezes 32
Description
Temperature

26. Example: Choose or
The temperature of a can of frozen juice about 2 __.
The temperature of a person with a fever is about __.
The temperature of a bowl of hot soup is about 175 __.
Solution:
a) b) c)

27. Conversions
To covert from Celsius to Fahrenheit use the following formula.
To covert from Fahrenheit to Celsius use the following formula.

28. Example: Conversions
The air temperature on a warm summer day is about What is the equivalent temperature on the Celsius thermometer?
Solution:
The equivalent temperature is about 29.4

29. Example: Conversions
The temperature of a cold glass of milk is about What is the equivalent temperature on the Fahrenheit thermometer?
Solution:
The equivalent temperature is about 41

30. Dimensional Analysis and Conversions to and from the Metric System
8.4
Dimensional Analysis and Conversions to and from the Metric System

31. 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:

32. U.S. Customary Units 1 pint = 2 cups 1 year = 365 days
1 cup (liquid) = 8 fluid ounces
1 day = 24 hours
1 ton = 2000 pounds
1 hour = 60 minutes
1 pound = 16 ounces
1 minute = 60 seconds
1 mile = 5280 feet
1 gallon = 4 quarts
1 yard = 3 feet
1 quart = 2 pints
1 foot = 12 inches
U.S. Customary Units

33. 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.

34. Conversion to and from the Metric System

35. 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 in2. What is its area in square centimeters?

36. 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 mi, 62 kpm is equivalent to mph.

37. 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 mg.