Copyright © 2005 Pearson Education, Inc. Chapter 2

Copyright © 2008 Pearson Education, Inc. Slide 2-2 Units The units of a quantity describe what is being measured or counted. Read kilowatts  hours as “kilowatt-hours.” hyphenMultiplication Read ft  ft  ft or ft 3, as “cubic feet” or “feet cubed” cube or cubicRaising to a third power Read ft  ft, or ft 2, as “square feet” or “feet squared” squareRaising to a second power Read miles  hours as “miles per hour” perDivision ExampleKey word or symbol Operation 2-A

epw 9/25/06 3 Solving Problems Unit Conversions

epw 9/25/06 4 Using Units Always keep units along with their quantities! Example ► 2500 watts x 3 hours = 7500 watt-hours ► Not 2500 x 3 = 7500 watt-hours Example ► 1000 watt-hours = 1 kilowatt-hour ►  500 watt-hours = 0.5 kilowatt-hour = 0.5 kw-hr

epw 9/25/06 5 Always keep units along with their quantities! Why

epw 9/25/06 6 Keep Units with their Quantities! Example: 12 ÷ 1 is not 1 But 12 inches ÷ 1 foot is 1, and 1 foot ÷ 12 inches is 1 because? 12 inches and 1 foot are equal!

12 Inches and 1 Foot are Equal Copyright © 2008 Pearson Education, Inc. Slide 2-7

epw 9/25/06 8 Different Ways of Writing 1

epw 9/25/06 9 Conversions Multiply, divide, or what? Simplify by multiplying by 1 Depends on what the problem is The key to solving the problem is knowing what units the solution should be Example, if the answer should be square yards (yd 2 ), and your solution produces yd 4, then your solution is incorrect

epw 9/25/06 10 Using Units Know the units to expect Examples The question asks for a cost in $  when using conversions, all units, except for dollars, should cancel! The question asks for speed in km/hr  when using conversions, all units, except for km/hr, should cancel!

epw 9/25/06 11 Conversion Format There are 12 inches per 1 foot: Also, there is 1 foot per 12 inches:  Use whatever produces the desired units!

epw 9/25/06 12 REPEAT! Know the units to expect Examples The question asks for a cost in $  when using conversions, all units, except for dollars, should cancel! The question asks for speed in km/hr  when using conversions, all units, except for km/hr, should cancel!

Copyright © 2008 Pearson Education, Inc. Slide 2-13 Unit Conversions Convert a distance of 9 feet into inches. 2-A

epw 9/25/06 14 Chain of Conversions If the problem doesn’t involve a simple conversion. such as “if you buy 2 pounds of apples when apples are 99 cents per pound, how much will you pay?” Use a chain of units conversions, where each step involves multiplying by 1

Copyright © 2008 Pearson Education, Inc. Slide 2-15 Chain of Units Conversions How many seconds are in one day? 2-A

Copyright © 2008 Pearson Education, Inc. Slide 2-16 Using a Chain of Conversions 2-A

Copyright © 2008 Pearson Education, Inc. Slide 2-17 Conversions with Units Raised to Powers 1 yd 2 = 1 yd × 1 yd = 3 ft × 3 ft = 9 ft 2 2-A

Copyright © 2008 Pearson Education, Inc. Slide 2-18 Cubic Units How many cubic yards of soil are needed to fill a planter that is 20 feet long by 3 feet wide by 4 feet tall? The volume is 20 ft × 3 ft × 4 ft = 240 ft 3 1 yd = 3 ft, so (1 yd) 3 = (3 ft) 3 = 27 ft 3 2-A

Copyright © 2008 Pearson Education, Inc. Slide 2-19 Currency Conversions 2-A You return from a trip to Europe with 120 euros. How many dollars do you have?

Copyright © 2008 Pearson Education, Inc. Slide 2-20 Problem Solving with Units You are buying 50 acres of farm land at a cost of $12,500 per acre. What is the total cost? The answer should be in dollars. We multiply acreage by the cost per acre: 2-A

Copyright © 2008 Pearson Education, Inc. Slide 2-21 U.S. Customary System 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-22 U.S. Customary System 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-23 U.S. Customary System 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-24 Metric Conversions 2-B 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)

Copyright © 2008 Pearson Education, Inc. Slide 2-25 USCS-Metric Conversions 2-B How many square miles are in 5 square kilometers? 1 km = mi, so (1 km) 2 = ( mi) 2 ≈ mi 2 5 km 2 ≈ 5 × mi 2 ≈ mi 2

Copyright © 2008 Pearson Education, Inc. Slide 2-26 Temperature Conversions The conversions are given in both words and with formulas in which C, F, and K are Celsius, Fahrenheit, and Kelvin temperatures, respectively. C = K  Subtract Kelvin to Celsius K = C Add Celsius to Kelvin Subtract 32. Then divide by 1.8 Fahrenheit to Celsius F = 1.8c + 32Multiply by 1.8. Then add 32. Celsius to Fahrenheit Conversion Formula Conversion in Words To Convert from 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-27 Units of Energy and Power Energy – makes matter move or heat up; international metric unit is the joule Power – the rate at which energy is used; international metric unit is the watt Kilowatt-hour – unit of energy; 1 kilowatt-hour = 3.6 million joules 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-28 Operating Cost of a Light Bulb 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? One watt = 1 joule/sec, so a 75 watt bulb uses 75 joules/sec. Find the number of joules used in a week: 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-29 Convert this result to kilowatt-hours: 2-B Now find the total cost:

Copyright © 2008 Pearson Education, Inc. Slide 2-30 Units of Density and Concentration Density describes compactness or crowding. Material density – given in units of mass per unit volume; i.e., g/cm 3 Population density – given by the number of people per unit area Information density – how much information can be stored by digital media 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-31 Units of Density and Concentration Concentration describes the amount of one substance mixed with another Concentration of an air pollutant – measured by the number of molecules of the pollutant per million molecules of air. Blood alcohol content – measured in units of grams of alcohol per 100 milliliters of blood. 2-B

Copyright © 2008 Pearson Education, Inc. Slide 2-32 Four Step Problem-Solving Process 2-C 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.

Copyright © 2008 Pearson Education, Inc. Slide 2-33 Problem Solving Guidelines and Hints 2-C Hint 1:There may be more than one answer. Hint 2:There may be more than one strategy. Hint 3:Use appropriate tools. Hint 4:Consider simpler, similar problems. Hint 5:Consider equivalent problems with simpler solutions. Hint 6:Approximations can be useful. Hint 7:Try alternative patterns of thought. Hint 8:Do not spin your wheels.

epw 9/10/06Copyright © 2005 Pearson Education, Inc. Slide 2-34 Problem Solving Example 2-C Find the total number of possible squares on the chessboard by looking for a pattern. Solution: Start with the largest possible square There is only one way to make an 8 x 8 square....

epw 9/10/06Copyright © 2005 Pearson Education, Inc. Slide 2-35 Problem Solving Example Find the total number of possible squares on the chessboard by looking for a pattern. Now, look for the number of ways to make a 7 x 7 square. There are only four ways.

epw 9/10/06Copyright © 2005 Pearson Education, Inc. Slide 2-36 Problem Solving Example 2-C If you continue looking at 6 x 6, 5 x 5 squares, and so on, you will discover the perfect square pattern for this chessboard problem as indicated in the table on the next slide Find the total number of possible squares on the chessboard by looking for a pattern.

epw 9/10/06Copyright © 2005 Pearson Education, Inc. Slide 2-37 Problem Solving Example 2-C Find the total number of possible squares on the chessboard by looking for a pattern.