Math for Liberal Arts MAT 110 : Chapter 2 Notes

Transcription

1 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

2 Section 2A: The Problem-Solving Power of Units What are some common unit labels? The Problem-Solving Power of Units Section 2A: The Problem-Solving Power of Units The units of a quantity describe what is being measured or counted. Conversion Factors A conversion factor is a statement of equality that is used to convert between units. Operation Division Key word or symbol per Example Read miles hours as miles per hour. Give me some examples. Raising to second power Raising to third power Multiplication square cube or cubic hyphen Read ft ft, or ft 2, as square feet or feet squared. Read ft ft ft, or ft 3, as cubic feet or feet cubed. Read kilowatts hours as kilowatt-hours. 2

3 Equivalent Forms of Conversion Factors Unit Conversions 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

4 Conversions of Units Raised to Powers Example 2.A.2: What is the conversion factor for cubic feet and cubic inches? Conversions of Units Raised to Powers Example 2.A.3: Convert 9 to cubic inches. Conversions of Units Raised to Powers Example 2.A.4:If 21.2 blahs = 4.1 ohhs Convert 20 ohhs to blahs. Currency Conversion $1.41 = yen = $1 Example 2.A.5: If you return from Europe with 145 euros, how many dollars do you have? 4

5 Standardized Unit Systems The International Metric System (or SI) Wide international use Standardized Units: More Problem-Solving Power U.S. Customary System (USCS) (or English system) Used in the United States U.S. Customary System U.S. Customary System 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

6 International Metric System 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: meter (m) for length gram (g) for mass second (s) for time liter (L) for volume Metric Conversions Moving between metric units requires shifting the decimal place one to the right when going to the next smaller unit and one to the left when going to the next larger unit. (Example: 5.23 cm = 52.3 mm) Metric Conversions Metric-USCS Conversions 10,000 mm =? Hm 10 KL =? dl 6

7 Metric-USCS Conversions Example 2.B.1:What is the conversion factor for square yards and square meter? Metric-USCS Conversions Example 2.B.2: In track and field, the 1600 meter race is often referred to as the mile. Are these terms really the same? Physics Conversions Example 2.B.3: Convert 30 to meters per second. Temperature Units Three temperature scales are commonly used today. A temperature of 0 is the coldest possible temperature, known as absolute zero. 7

8 Units of Energy and Power Energy is what makes matter move or heat up. International metric unit is the joule 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 Operating cost of a Light Bulb Example 2.B.4: A utility company charges 12.5 per kilowatt-hour of electricity. How much does it cost to keep a 75-watt light bulb on for a week? Units of Density and Concentration Density describes compactness or crowding Material density is given in units of mass per unit volume. e.g., grams per cubic centimeter ( ) Population density is given by the number of people per unit area. e.g., people per square mile ( ) Information density is given in units of mass per unit volume. e.g., gigabytes per square inch ( ) Units of Density and Concentration Concentration describes the amount of one substance mixed with another. The concentration of an air pollutant is often measured by the number of molecules of the pollutant per million molecules of air. e.g., parts per million (ppm) Blood alcohol content (BAC) describes the concentration of alcohol in a person s body. e.g., grams of alcohol per 100 milliliters of blood 8

9 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-Solving Guidelines and Hints Four Step Problem-Solving Process Step 1: Step 2: Step 3: Step 4: Understand the problem. Devise a strategy for solving the problem. Carry out your strategy, and revise if necessary. Look back to check, interpret, and explain your result. Problem Solving Example 2.C.1: Find the total number of possible squares on the chessboard. 9

10 Ticket Sales 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 Example 2.C.3: You are going to buy a condo and have the choice of a deck or no deck, and granite, marble or quartz countertops. How many possible combinations are there? MyMathLab Be sure that you are keeping up on your homework on MyMathlab. 10