1. Vocabulary
Conversion Factor

2. Conversion Factor A ratio of equivalent measurements
Example: 100cm/1m = 1m/1m = 1
60min/1hr = 1

3. Christopher G. Hamaker, Illinois State University, Normal IL
The Metric System
Christopher G. Hamaker, Illinois State University, Normal IL
© 2005, Prentice Hall

4. The Metric System
The English System was used primarily in the British Empire and wasn’t very standardized.
The French organized a committee to devise a universal measuring system.
After about 10 years, the committee designed and agreed on the metric system.
The metric system offers simplicity with a single base unit for each measurement.

5. Basic Units in the Metric System
Metric Base Units
Basic Units in the Metric System
Physical Quantity
Basic Unit
Symbol
Length
meter m
Mass
gram g
Volume
liter L
Time
Energy
Amount of Matter
Second
Joule
Mole S J
mol

6. Metric System Advantage
Another advantage of the metric system is that it is a decimal system.
It uses prefixes to enlarge or reduce the basic units.
For example:
A kilometer is 1000 meters.
A centimeter is 1/100 of a meter.

7. Metric System Prefixes
The following table lists the common prefixes used in the metric system:

8. Metric Prefixes Continued
For example, the prefix kilo- increases a base unit by 1000:
1 kilogram is 1000 grams.
The prefix centi- decreases a base unit by a factor of 100:
1 centimeter is 0.01 meters.

9. Metric Symbols
The names of metric units are abbreviated using symbols. Use the prefix symbol followed by the symbol for the base unit, so:
kilometer is abbreviated km.
milligram is abbreviated mg.
microliter is abbreviated mL.
nanosecond is abbreviated ns.

10. Metric Equivalents
We can write unit equations for the conversion between different metric units.
The prefix kilo- means 1000 basic units, so 1 kilometer is 1000 meters.
The unit equation is 1 km = 1000m.
Similarly, a centimeter is 1/100 of a meter, so the unit equation is 1 cm = 0.01 m.

11. Temperature
Temperature is a measure of the average kinetic energy of the individual particles in a sample.
There are three temperature scales:
Celsius
Fahrenheit
Kelvin
Kelvin is the absolute temperature scale.

12. Temperature Scales
On the Fahrenheit scale, water freezes at 32°F and boils at 212°F.
On the Celsius scale, water freezes at 0°C and boils at 100°C. These are the reference points for the Celsius scale.
Water freezes at 273K and boils at 373K on the Kelvin scale.

13. Temperature Conversions
This is the equation for converting °C to °F.
This is the equation for converting °F to °C.
To convert from °C to K, add 273.
°C = K
= °F °C 5 9
( )
( )
F-32
= °C 9 5

14. Fahrenheit-Celsius Conversions
Body temperature is 98.6°F. What is body temperature in Celsius?
( ) 9 5
= 37.0°C
(98.6°F - 32°F) ×

15. Unit Equations
A unit equation is a simple statement of two equivalent quantities.
For example:
1 hour = 60 minutes
1 minute = 60 seconds
Also, we can write:
1 minute = 1/60 of an hour
1 second = 1/60 of a minute

16. Unit Conversions
A unit conversion factor, or unit factor, is a ratio of two equivalent options.
For the unit equation 1 hour = 60 minutes, we can write two unit factors:
1 hour or minutes
60 minutes hour

17. Unit Analysis Problem Solving
An effective method for solving problems in science is the unit analysis method.
It is also often called dimensional analysis or the factor label method.
There are three steps to solving problems using the unit analysis method.

18. Steps in the Unit Analysis Method
Write down the unit asked for in the answer
Write down the given value related to the answer.
Apply a unit factor to convert the unit in the given value to the unit in the answer.

19. Unit Analysis Problem How many days are in 2.5 years?
Step 1: We want days.
Step 2: We write down the given: 2.5 years.
Step 3: We apply a unit factor (1 year = 365 days) and round to two significant figures.

20. Another Unit Analysis Problem
A can of Coca-Cola contains 12 fluid ounces. What is the volume in quarts (1 qt = 32 fl oz)?
Step 1: We want quarts.
Step 2: We write down the given: 12 fl oz.
Step 3: We apply a unit factor (1 qt = 32 fl oz) and round to two significant figures.

21. Another Unit Analysis Problem
A marathon is 26.2 miles. What is the distance in yards (1 mi = 1760 yards)?
Step 1: We want yards.
Step 2: We write down the given: 26.2 miles.
Step 3: We apply a unit factor (1 mi = 1760 yards) and round to three significant figures.

22. Metric Unit Factors
Since 1000 m = 1 km, we can write the following unit factors for converting between meters and kilometers:
1 km or m
1000 m km
Since 1 m = 0.01 cm, we can write the following unit factors.
1 cm or m
0.01 m cm

23. Metric-Metric Conversions
We will use the unit analysis method we learned in Chapter 2 to do metric-metric conversion problems.
Remember, there are three steps
Write down the unit asked for in the answer
Write down the given value related to the answer
Apply unit factor(s) to convert the given unit to the units desired in the answer.

24. Metric-Metric Conversion Problem
What is the mass in grams of a 325 mg aspirin tablet?
Step 1: We want grams.
Step 2: We write down the given: 325 mg.
Step 3: We apply a unit factor (1 mg = g) and round to three significant figures.
325 mg ×
= g
1 mg
0.001 g

25. Metric and English Units
The English system is still very common in the United States.
We often have to convert between English and Metric Units.

26. Metric-English Conversion
Which distance is longer, 100 meters or 100 yards?
Lets convert m to 100 yards given that yd = m.
100 meters is 109 yards, so 100 yards is shorter.
100.0 m ×
= 109 yd
0.914 m
1 yd

27. English-Metric Conversion
A half gallon carton contains 64.0 fl oz of milk. How many milliliters of milk are in a carton?
We want mL, we have 64.0 fl oz.
Use 1 qt = 32 fl oz, and 1 qt = 946 mL.
64.0 fl oz ×
= 1,890 mL ×
32 fl oz
1 qt
946 mL

28. Compound Unit Problem
A Corvette is traveling at 95 km/hour. What is the speed in meters per second?
We have km/h, we want m/s.
Use 1 km = 1000 m and 1 h = 3600 s.
= 26 m/s ×
1 km
1000 m
1 hr
3600 s
95 km hr