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

Unit Definitions

• A meter was defined as 1/10,000,000 of the distance from the North Pole to the equator.

• A kilogram (1000 grams) was equal to the mass of a cube of water measuring 0.1 m on each side.

• A liter was set equal to the volume of one kilogram of water at 4C.

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 ×100°C180°F( )

( )180°F100°C

= °C(°F - 32°F) ×

Fahrenheit-Celsius Conversions

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

( )180°F100°C

= 37.0°C(98.6°F - 32°F) ×

Heat

• Heat is the flow of energy from an object of higher temperature to an object of lower temperature.

• Heat measures the total energy of a system while temperature measures the average energy of particles in a system.

• Heat is often expressed in terms of joules (J) or calories (cal).

Volume by Calculation

• The volume of an object is calculated by multiplying the length (l) by the width (w) by the thickness (t).

volume = l × w × t

• All three measurements must be in the same units.

• If an object measures 3 cm by 2 cm by 1 cm, the volume is 6 cm3 (cm3 is cubic centimeters).

Cubic Volume vs. Liquid Volume

• The liter (L) is the basic unit of volume in the metric system.

• One liter is defined as the volume occupied by a cube that is 10 cm on each side.

Cubic & Liquid Volume Units

• 1 liter is equal to 1000 cubic centimeters

– 10 cm × 10 cm × 10 cm = 1000 cm3

• 1000 cm3 = 1 L = 1000 mL.

• Therefore, 1 cm3 = 1 mL.

Volume by Displacement

• If a solid has an irregular shape, its volume cannot be determined by measuring its dimensions.

• You can determine its volume indirectly by measuring the amount of water it displaces.

• This technique is call volume by displacement.

Volume by Displacement• You want to measure the volume of an irregularly

shaped piece of jade.

• Partially fill a volumetric flask with water and measure the volume of the water.

• Add the jade, and measure the difference in volume.

• The volume of the jade is 10.5 mL.

The Density Concept

• The density of an object is a measure of its concentration of mass

• Density is defined as the mass of an object divided by the volume of the object.

= densityvolumemass

Density

• Density is expressed in different units. It is usually grams per milliliter (g/mL) for liquids, grams per cubic centimeter (g/cm3) for solids, and grams per liter (g/L) for gases.

Estimating Density

• We can estimate the density of a substance by comparing it to another object.

• A solid object will float on top a liquid with a higher density.

• Object S1 has a density less than that of water, but larger than that of L1.

• Object S2 has a density less than that of L2, but larger than that of water.

Calculating Density

• What is the density of a platinum nugget has a mass of 224.50 g and a volume of 10.0 cm3 ?

• Recall, density is mass/volume.

= 22.5 g/cm3

10.0 cm3

224.50 g

Specific Heat

• The specific heat of a substance is the amount of heat required to bring about a change in temperature.

• It is expressed with units of calories per gram degree Celsius.

• The larger the specific heat, the more heat is required to raise the temperature of the substance.

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

Two Metric-Metric Conversions

• A hospital has 125 deciliter bags of blood plasma. What is the volume in milliliters?

• Step 1: we want the answer in mL

• Step 2: we have 125 dL.

• Step 3: we need to first convert dL to L and then convert L to mL:

0.1 L and 0.001 mL1 dL 1 L .

Problem Continued• Apply both unit factors, and round the answer to 3

significant digits.

• Notice that both dL and L units cancel, leaving us with units of mL.

125 dL × = 12,500 mL×1 dL0.1 L 1 mL

0.001 L

Another Example

• The mass of the Earth is 5.98 × 1024 kg. What is the mass expressed in megagrams, Mg?

• We want Mg; we have 5.98 × 1024 kg

• Convert kilograms to grams, and then grams to megagrams.

5.98 × 1024 kg × = 5.98 × 1021 Mg×1 kg

1000 g 1 Mg

1000000 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

English-Metric Conversion

• A Volkswagen Beetle engine displaces a volume of 498 cm3 in each cylinder. What is the displacement in cubic inches, in3?

• We want in3, we have 498 cm3.

• Use 1 in = 2.54 cm three times.

= 30.4 in3×1 in

2.54 cm ×498 cm3 ×

1 in2.54 cm

1 in2.54 cm

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

×

Density as a Unit Factor

• We can use density as a unit factor for conversions between mass and volume.

• An automobile battery contains 1275 mL of acid. If the density of battery acid is 1.84 g/mL, how many grams of acid are in an automobile battery?

• We have 1275 mL and we want grams:

1275 mL × = 2350 gmL

1.84 g

Conclusions

• The basic units in the metric system are grams for mass, liters for volume, and meters for distance.

• The base units are modified using prefixes to reduce or enlarge the base units by factors of 10.

• We can use unit factors to convert between metric units.

• We can convert between metric and English units using unit factors.

Summary Continued

• A unit equation is a statement of two equivalent quantities.

• A unit factor is a ratio of two equivalent quantities.

• Unit factors can be used to convert measurements between different units.

Conclusions Continued

• Volume is defined as length × width × thickness.

• Volume can also be determined by displacement of water.

• Density is mass divided by volume.

Conclusions Continued

• Temperature is a measure of the average energy of the particles in a sample.

• Heat is a measure of the total energy of a substance.

• Specific heat is a measure of how much heat is required to raise the temperature of a substance.