Chapter 2 Measurements 2.7 Problem Solving Using Unit Conversions Learning Goal Use conversion factors to change from one unit to another. © 2014 Pearson Education, Inc.

Problem-Solving Process The problem-solving process begins by analyzing the problem in order to identify the given unit and needed unit write a plan that converts the given unit to the needed unit identify one or more conversion factors that cancel units and provide the needed unit set up a calculation © 2014 Pearson Education, Inc.

Suppose you need to convert 18.2 mm to meters. Setting up the Problem Suppose you need to convert 18.2 mm to meters. First, identify the given and needed units. Given: 18.2 m Need: meters Write a plan that will convert the given unit to the needed unit. millimeter Conversion meters Given factor Need © 2014 Pearson Education, Inc.

Look for the connection between millimeters and meters. 1 m = 1000 mm Setting up the Problem Look for the connection between millimeters and meters. 1 m = 1000 mm From this equality, we can write two conversion factors. © 2014 Pearson Education, Inc.

millimeters conversion factor meters Setting up the Problem Select the conversion factor that cancels the given unit, which is the millimeter. Complete the calculation and round off to the needed significant figures. millimeters conversion factor meters © 2014 Pearson Education, Inc.

Guide to Problem Solving Using Conversion Factors © 2014 Pearson Education, Inc.

How many minutes are in 2.5 h? Learning Check How many minutes are in 2.5 h? © 2014 Pearson Education, Inc.

How many minutes are in 2.5 h? Solution How many minutes are in 2.5 h? Step 1 State the given and needed quantities. Given: 2.5 h Need: minutes Step 2 Write a plan to convert the given unit to the needed unit. hours Conversion factor minutes Given Need © 2014 Pearson Education, Inc.

How many minutes are in 2.5 h? Solution How many minutes are in 2.5 h? Step 3 State the equalities and conversion factors. 1 h = 60 min Step 4 Set up the problem to cancel units and calculate. © 2014 Pearson Education, Inc.

Using Two or More Conversion Factors Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1  Unit 2  Unit 3 Additional conversion factors are placed in the setup to cancel each preceding unit. Given unit × factor 1 × factor 2 = needed unit © 2014 Pearson Education, Inc.

How many minutes are in 1.4 days? Step 1 Given 1.4 days Need minutes Sample Problem How many minutes are in 1.4 days? Step 1 Given 1.4 days Need minutes Step 2 Plan days  hours  minutes Step 3 Equalities 1 day = 24 h 1 h = 60 min Conversion Factors © 2014 Pearson Education, Inc.

How many minutes are in 1.4 days? Step 4 Set up problem, cancel units. Sample Problem How many minutes are in 1.4 days? Step 4 Set up problem, cancel units. © 2014 Pearson Education, Inc.

A bucket contains 4.65 L water. How many gallons of water is that? Learning Check A bucket contains 4.65 L water. How many gallons of water is that? © 2014 Pearson Education, Inc.

A bucket contains 4.65 L water. How many gallons of water is that? Solution A bucket contains 4.65 L water. How many gallons of water is that? Step 1 Given 4.65 L Need gallons Step 2 Plan liters  quarts  gallons Step 3 Equalities 1 L = 1.057 qt 1 gal = 4 qt Conversion Factors © 2014 Pearson Education, Inc.

Step 4 Set up problem, cancel units. Solution Step 4 Set up problem, cancel units. © 2014 Pearson Education, Inc.