8/24/2012 A Quick Fractions Review • Adding & Subtracting Math for Liberal Arts MAT 110 : Chapter 2 Notes David J. Gisch A Quick Fractions Review Percents and Decimals • Multiplying and Dividing 1
8/24/2012 S ection 2A: The Problem-S olving Power of Units • What are some common unit labels? The Problem-Solving Power of Units Conversion Factors S ection 2A: The Problem-S olving Power of Units The units of a quantity describe what is being A conversion factor is a statement of equality measured or counted. that is used to convert between units. Give me some examples. Operation Key word or Exam ple sym bol Read miles hours as “miles Division per per hour.” Read ft ft, or ft 2 , as Raising to second square power “square feet” or “feet squared.” Raising to third power cube or cubic Read ft ft ft, or ft 3 , as “cubic feet” or “feet cubed.” Read kilowatts hours as Multiplication hyphen “kilowatt-hours.” 2
8/24/2012 Unit Conversions Equivalent Forms of Conversion Factors • Use the form of the conversion factor that allows you to cancel labels. Example 2.A.1: Convert each of the following. (a) 8 in. to feet. (b)55 inches to meters A Chain of Conversions Conversions of Units Raised to Powers 3
8/24/2012 Conversions of Units Raised to Powers Conversions of Units Raised to Powers Example 2.A.3: Convert 9 �� � to cubic inches. Example 2.A.2: What is the conversion factor for cubic feet and cubic inches? Conversions of Units Raised to Powers Currency Conversion Example 2.A.4:If 21.2 blahs = 4.1 ohhs $1.41 = 1 ₤ Convert 20 ohhs to blahs. 99.34 yen = $1 Example 2.A.5: If you return from Europe with 145 euros, how many dollars do you have? 4
8/24/2012 S tandardized Unit S ystems The International Metric System (or SI) ▫ Wide international use U.S. Custom ary System (USCS) (or English system) S tandardized Units: More Problem-S olving Power ▫ Used in the United States U.S . Customary S ystem U.S . Customary S ystem • Units of length were based on individual body measurements. ▫ A foot was once the length of the measurer’s foot. ▫ An inch was the thumb-width of the measurer. ▫ A mile was one thousand paces. • There are three distinct sets of units used to measure weight. 1. Jewelers used troy measures of weight. 2. Pharmacists used apothecary measures of weight. 3. Other commerce was conducted with avoirdupois measures of weight. • The basic unit of volume is the cubic inch (in. 3 ). Dry and liquid measures differ. ▫ 5
8/24/2012 International Metric S ystem Metric Conversions • The metric system was designed to 1. replace many customary units with a few basic units. 2. simplify conversions through the use of a decimal (base 10) system. • The following are basic metric units: m eter (m) for length ▫ gram (g) for mass ▫ second (s) for time ▫ Moving between metric units requires shifting the decimal place liter (L) for volume ▫ one to the right when going to the next sm aller unit and one to the left when going to the next larger unit. (Example: 5.23 cm = 52.3 mm) Metric Conversions Metric-US CS Conversions 10,000 mm = ? Hm 10 KL = ? dL 6
8/24/2012 Metric-US CS Conversions Metric-US CS Conversions Example 2.B.1:What is the conversion factor for Example 2.B.2: In track and field, the 1600 meter square yards and square meter? race is often referred to as the mile. Are these terms really the same? Physics Conversions Temperature Units Example 2.B.3: Convert 30 ��� to meters per Three temperature scales are commonly used today. second. A temperature of 0 � is the coldest possible temperature, known as absolute zero . 7
8/24/2012 Units of Energy and Power Operating cost of a Light Bulb Example 2.B.4: A utility company charges 12.5¢ • Energy is what makes matter move or heat up. per kilowatt-hour of electricity. How much does it ▫ International metric unit is the joule cost to keep a 75-watt light bulb on for a week? • Power is the rate at which energy is used. ▫ International metric unit is the watt 1 watt � 1 j s � • A kilowatt-hour is a unit of energy. 1 �������� � ���� � 3.6 ������� ������ Units of Density and Concentration Units of Density and Concentration Density describes compactness or crowding Concentration describes the amount of one substance mixed with another. • Material density is given in units of mass per unit volume. • The concentration of an air pollutant is often ▫ e.g., grams per cubic centimeter ( � �� � ⁄ ) measured by the number of molecules of the • Population density is given by the number of pollutant per million molecules of air. people per unit area. ▫ e.g., parts per m illion (ppm ) ▫ e.g., people per square mile ( ������ �� � ⁄ ) • Blood alcohol content (BAC) describes the • Inform ation density is given in units of mass per concentration of alcohol in a person’s body. unit volume. ▫ e.g., gram s of alcohol per 100 m illiliters of blood ▫ e.g., gigabytes per square inch ( �� �� � ⁄ ) 8
8/24/2012 Population Density Example 2.B.5: The land area of the United States is about 3.5 million square miles, and the population is about 300 million people. What is the average population density? Problem-S olving Guidelines and Hints Four S tep Problem-S olving Process Problem S olving Example 2.C.1: Find the total number of possible squares on the chessboard. Step 1: Understand the problem. Step 2: Devise a strategy for solving the problem. Step 3: Carry out your strategy, and revise if necessary. Step 4: Look back to check, interpret, and explain your result. 9
8/24/2012 Ticket S ales Example 2.C.2: A school is putting on a play and they are selling tickets at a cost of $8 for adults and $5 for students. If they sold $68 worth of tickets, how many of each kind did they sell? A Condo MyMathLab Example 2.C.3: You are going to buy a condo and • Be sure that you are keeping up on your have the choice of a deck or no deck, and granite, homework on MyMathlab. marble or quartz countertops. How many possible ▫ www.pearsonmylab.com combinations are there? 10
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