1. Chapter 2 Measurements 2.7 Problem Solving Using Unit Conversions
Learning Goal Use conversion factors to change from one unit to another.
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2. 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
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3. 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: m Need: meters
Write a plan that will convert the given unit to the needed unit.
millimeter Conversion meters
Given factor Need
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4. 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.
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5. 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
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6. Guide to Problem Solving Using Conversion Factors
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7. How many minutes are in 2.5 h?
Learning Check
How many minutes are in 2.5 h?
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8. 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
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9. 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.
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10. 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
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11. 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
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12. 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.
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13. 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?
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14. 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 L Need gallons
Step 2 Plan liters  quarts  gallons
Step 3 Equalities 1 L = qt 1 gal = 4 qt
Conversion Factors
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15. Step 4 Set up problem, cancel units.
Solution
Step 4 Set up problem, cancel units.
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