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

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 4  C.

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 minutes 60 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.

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.

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.

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 = g) and round to three significant figures. 325 mg ×= g 1 mg 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 mL 1 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 dL 0.1 L 1 mL L

Another Example The mass of the Earth is 5.98 × kg. What is the mass expressed in megagrams, Mg? We want Mg; we have 5.98 × kg Convert kilograms to grams, and then grams to megagrams × kg ×= 5.98 × Mg× 1 kg 1000 g 1 Mg 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 m to 100 yards given that 1 yd = m. 100 meters is 109 yards, so 100 yards is shorter m ×= 109 yd 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 fl oz ×= 1,890 mL× 32 fl oz 1 qt 946 mL 1 qt

English-Metric Conversion A Volkswagen Beetle engine displaces a volume of 498 cm 3 in each cylinder. What is the displacement in cubic inches, in 3 ? We want in 3, we have 498 cm 3. Use 1 in = 2.54 cm three times. = 30.4 in 3 × 1 in 2.54 cm ×498 cm 3 × 1 in 2.54 cm 1 in 2.54 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 hr 3600 s 95 km hr ×

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 g mL 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.