Slide Copyright © 2009 Pearson Education, Inc. Unit 5 The Metric System

Slide Copyright © 2009 Pearson Education, Inc. SI System and U.S. Customary System Most countries of the world use the Systéme international d’unités or SI system, 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. 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.

Slide Copyright © 2009 Pearson Education, Inc. Basic Terms a little more than a quart volumeLliter about 2.2 pounds masskgkilogram a little more than a yard lengthmmeter Comparison to Customary Common Use AbbrevMetric Term

Slide Copyright © 2009 Pearson Education, Inc. Metric Prefixes 1/1000 of base unitmmilli 1/100 of base unitccenti 1/10 of base unitddeci base unit 10 x base unitdadeka 100 x base unithhecto 1000 x base unitkkilo MeaningSymbolPrefix

Slide Copyright © 2009 Pearson Education, Inc. Changing Units within the Metric System Measure of length kilometerhectometerdekameter Symbolkmhmdam Number of meters 1000 m100 m10 m Measure of length meterdecimetercentimetermillimeter Symbolmdmcmmm Number of meters 1 m0.1 m0.01 m0.001 m

Slide Copyright © 2009 Pearson Education, Inc. 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.

Slide Copyright © 2009 Pearson Education, Inc. 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, km. Liter is a larger unit than milliliter. Move the decimal point 3 places to the right, 15,000 mL. Kilogram is a larger unit than centigram. Move the decimal point 5 places to the right 0.89 kg = 89,000 cg

Slide Copyright © 2009 Pearson Education, Inc. 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 holds 250 mL, then 72 glasses can be filled.

Slide Copyright © 2009 Pearson Education, Inc. 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.

Slide Copyright © 2009 Pearson Education, Inc. 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 x width.

Slide Copyright © 2009 Pearson Education, Inc. 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. When the volume of a liquid is measured, the abbreviation cc is often used instead of cm 3 to represent cubic centimeters. 1 m 3 = 1 kL 1 dm 3 = 1 L 1 cm 3 = 1 mL Volume in LitersVolume in Cubic Units

Slide Copyright © 2009 Pearson Education, Inc. 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:

Slide Copyright © 2009 Pearson Education, Inc. 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.

Slide Copyright © 2009 Pearson Education, Inc. 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 (t) is used to express mass of heavy items. One metric tonne = 1000 kg.

Slide Copyright © 2009 Pearson Education, Inc. Volume and Mass of Water Volume in Cubic Units 1 m 3 = 1 kL = 1 t (1000 kg) 1 dm 3 = 1 L = 1 kg 1 cm 3 = 1 mL = 1 g Mass of WaterVolume in Liters

Slide Copyright © 2009 Pearson Education, Inc. 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. Solution: Since 1 m 3 of water = 1 kL of water, m 3 = kL, or 156 liters of water Since 1L = 1 kg, 156 L = 156 kg of water.

Slide Copyright © 2009 Pearson Education, Inc. Temperature The term degrees Celsius (ºC) is used to measure temperature. Water boils212ºF100ºC Body temperature98.6ºF37ºC Comfortable room71.6ºF22ºC Water freezes32ºF0ºC Description ºFºC Temperature

Slide Copyright © 2009 Pearson Education, Inc. Conversions To covert from Celsius to Fahrenheit use the following formula. To covert from Fahrenheit to Celsius use the following formula.

Slide Copyright © 2009 Pearson Education, Inc. Example: Conversions The air temperature on a warm summer day is about 85ºF. What is the equivalent temperature on the Celsius thermometer? Solution: The equivalent temperature is about 29.4ºC.

Slide Copyright © 2009 Pearson Education, Inc. Example: Conversions The temperature of a cold glass of milk is about 5ºC. What is the equivalent temperature on the Fahrenheit thermometer? Solution: The equivalent temperature is about 41ºF.

Slide Copyright © 2009 Pearson Education, Inc. 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:

Slide Copyright © 2009 Pearson Education, Inc. U.S. Customary Units 1 pint = 2 cups 1 year = 365 days 1 cup (liquid) = 8 fluid ounces 1 day = 24 hours1 ton = 2000 pounds 1 hour = 60 minutes1 pound = 16 ounces 1 minute = 60 seconds1 mile = 5280 feet 1 gallon = 4 quarts1 yard = 3 feet 1 quart = 2 pints1 foot = 12 inches U.S. Customary Units

Slide Copyright © 2009 Pearson Education, Inc. 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. Solution:

Slide Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Length LENGTH U.S. to Metric 1 inch (in.) ≈ 2.54 centimeters (cm) 1 foot (ft) ≈ 30 centimeters (cm) 1 yard (yd) ≈ 0.9 meter (m) 1 mile (mi) ≈ 1.6 kilometers (km)

Slide Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Area AREA U.S. to Metric 1 square inch (in. 2 ) ≈ 6.5 square centimeters (cm 2 ) 1 square foot (ft 2 ) ≈ 0.09 square meter (m 2 ) 1 square yard (yd 2 ) ≈ 0.8 square meter (m 2 ) 1 square mile (mi 2 ) ≈ 2.6 square kilometers (km 2 ) 1 acre ≈ 0.4 hectare (ha)

Slide Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Volume VOLUME U.S. to Metric 1 teaspoon (tsp) ≈ 5 milliliters (m l ) 1 tablespoon (tbsp) ≈ 15 milliliters (m l ) 1 fluid ounce (fl oz) ≈ 30 milliliters (m l ) 1 cup (c) ≈ 0.24 liter ( l ) 1 pint (pt) ≈ 0.47 liter ( l )

Slide Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Volume VOLUME U.S. to Metric 1 quart (qt) ≈ 0.95 liter ( l ) 1 gallon (gal) ≈ 3.8 liters ( l ) 1 cubic foot (ft 3 ) ≈ 0.03 cubic meter (m 3 ) 1 cubic yard (yd 3 ) ≈ 0.76 cubic meter (m 3 )

Slide Copyright © 2009 Pearson Education, Inc. Conversion to and from the Metric System - Weight (Mass) WEIGHT OR MASS U.S. to Metric 1 ounce (oz) ≈ 28 grams (g) 1 pound (lb) ≈ 0.45 kilogram (kg) 1 ton (T) ≈ 0.9 tonne (t)

Slide Copyright © 2009 Pearson Education, Inc. 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 in 2. What is its area in square centimeters? Solution:

Slide Copyright © 2009 Pearson Education, Inc. 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 kph is equivalent to mph.

Slide Copyright © 2009 Pearson Education, Inc. 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.