1 Chapter 1 Measurements 1.6 Problem Solving Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

2 To solve a problem Identify the given unit Identify the needed unit. Example: A person has a height of 2.0 meters. What is that height in inches? The given unit is the initial unit of height. given unit = meters (m) The needed unit is the unit for the answer. needed unit = inches (in.) Given and Needed Units

3 Learning Check An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the given and needed units given in this problem. Given unit= _______ Needed unit = _______

4 Solution An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the given and needed units given in this problem. Given unit= pints Needed unit = milliliters

5 Write the given and needed units. Write a unit plan to convert the given unit to the needed unit. Write equalities and conversion factors that connect the units. Use conversion factors to cancel the given unit and provide the needed unit. Unit 1 x Unit 2 = Unit 2 Unit 1 Given x Conversion= Needed unit factor unit Problem Setup

6 Guide to Problem Solving The steps in the Guide to Problem Solving are useful in setting up a problem with conversion factors.

7 How many minutes are 2.5 hours? Given unit= 2.5 hr Needed unit=min Unit Plan=hr min Setup problem to cancel hours (hr). Given Conversion Needed unit factor unit 2.5 hr x 60 min = 150 min ( 2 SF ) 1 hr Setting up a Problem Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

8 A rattlesnake is 2.44 m long. How many centimeters long is the snake? 1) 2440 cm 2)244 cm 3)24.4 cm Learning Check

9 A rattlesnake is 2.44 m long. How many centimeters long is the snake? 2)244 cm Given Conversion Needed unit factor unit 2.44 m x 100 cm = 244 cm 1 m Solution

10 Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2Unit 3 Additional conversion factors are placed in the setup to cancel each preceding unit Given unit x factor 1 x factor 2 = needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2 Using Two or More Factors

11 How many minutes are in 1.4 days? Given unit: 1.4 days Factor 1 Factor 2 Plan: days hr min Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 10 3 min 1 day 1 hr 2 SF Exact Exact = 2 SF Example: Problem Solving

12 Be sure to check your unit cancellation in the setup. The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x 1 hr 24 hr 60 min Units = day 2 /min is not the unit needed Units don’t cancel properly. Check the Unit Cancellation

13 Using the GPS What is 165 lb in kg? STEP 1 Given 165 lb Need kg STEP 2 Plan STEP 3 Equalities/Factors 1 kg = 2.20 lb 2.20 lb and 1 kg 1 kg 2.20 lb STEP 4 Set Up Problem 165 lb x 1 kg = 75.0 kg 2.20 lb

14 A bucket contains 4.65 L of water. How many gallons of water is that? Unit plan: L qt gallon Equalities:1.06 qt = 1 L 1 gal = 4 qt Set up Problem: Learning Check

15 Given: 4.65 L Needed: gallons Plan: L qt gallon Equalities: 1.06 qt = 1 L; 1 gal = 4 qt Set Up Problem: 4.65 L x x 1.06 qt x 1 gal = 1.23 gal 1 L 4 qt 3 SF 3 SF exact 3 SF Solution

16 If a ski pole is 3.0 feet in length, how long is the ski pole in mm? Learning Check

ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm Calculator answer: mm Needed answer:910 mm (2 SF rounded) Check factor setup: Units cancel properly Check needed unit: mm Solution

18 If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet? Learning Check

19 Solution Given: 7500 ft65 m/minNeed: min Plan: ft in. cm m min Equalities: 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm 1 min = 65 m (walking pace) Set Up Problem: 7500 ft x 12 in. x 2.54 cm x 1m x 1 min 1 ft 1 in. 100 cm 65 m = 35 min final answer (2 SF)

20 Percent Factor in a Problem Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg? percent factor 86 kg mass x 11 kg fat 100 kg mass = 9.5 kg fat

21 How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Learning Check

22 Solution How many lb of sugar are in 120 g of candy if the candy is 25%(by mass) sugar? percent factor 120 g candy x 1 lb candy x 25 lb sugar 454 g candy 100 lb candy = lb sugar