Vocabulary

• Conversion Factor

Conversion Factor

A ratio of equivalent measurements

Example: 100cm/1m = 1m/1m = 1

60min/1hr = 1

Christopher G. Hamaker, Illinois State University, Normal IL© 2005, Prentice Hall

The Metric SystemThe Metric System

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.

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

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.

Metric System Prefixes• The following table lists the common prefixes

used in the metric system:

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.

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 L.

– nanosecond is abbreviated ns.

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.

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.

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.

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 + 273 = K

= °F°C + 3259( )

( )F-32 = °C9

5

Fahrenheit-Celsius Conversions

• Body temperature is 98.6°F. What is body temperature in Celsius?

( )95 = 37.0°C(98.6°F - 32°F) ×

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

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 60 minutes60 minutes 1 hour

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.

Steps in the Unit Analysis Method

1. Write down the unit asked for in the answer

2. Write down the given value related to the answer.

3. Apply a unit factor to convert the unit in the given value to the unit in the answer.

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.

days910year1

days365years2.5

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.

qt 38.0oz. fl23

qt 1oz. fl21

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.

yd 100,46mi1

yd 1760mi2.26

Metric Unit Factors

• Since 1000 m = 1 km, we can write the following unit factors for converting between meters and kilometers:

1 km or 1000 m 1000 m 1 km

• Since 1 m = 0.01 cm, we can write the following unit factors.

1 cm or 0.01 m 0.01 m 1 cm

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.

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 = 0.001 g) and round to three significant figures.

325 mg × = 0.325 g1 mg

0.001 g

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.

Metric-English Conversion

• Which distance is longer, 100 meters or 100 yards?

• Lets convert 100.0 m to 100 yards given that 1 yd = 0.914 m.

• 100 meters is 109 yards, so 100 yards is shorter.

100.0 m × = 109 yd0.914 m

1 yd

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 mL1 qt

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 hr3600 s

95 kmhr

×