1. Chapter 2 Measurements 2.7 Problem Solving
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Publishing as Benjamin Cummings

2. Given and Needed Units To solve a problem: Identify the given unit
Identify the needed unit
Problem: 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)

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 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 in this problem
Given unit = pints
Needed unit = milliliters

5. Problem Setup 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 x Unit = Unit 2
Unit 1
Given x Conversion = Needed
unit factor unit

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

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

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

9. Solution
A rattlesnake is 2.44 m long. How many centimeters long is the snake?
2) 244 cm
2.44 m x cm = 244 cm
1 m

10. Using Two or More 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 x factor 1 x factor 2 = needed unit
Unit x Unit x Unit = Unit 3
Unit Unit 2

11. Example: Problem Solving
How many minutes are in 1.4 days?
Given unit: 1.4 days
Factor Factor 2
Plan: days hr min
Set up problem:
1.4 days x 24 hr x 60 min = 2.0 x 103 min
1 day hr
2 SF Exact Exact = 2 SF

12. Check the Unit Cancellation
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 hr
24 hr min
Units = day2/min is Not the unit needed
Units don’t cancel properly.

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 = lb
2.205 lb and kg
1 kg lb
STEP 4 Set Up Problem

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

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

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

17. Solution 3.0 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

18. Learning Check 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?

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

20. Percent Factor in a Problem
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 kg fat
100 kg mass
= 9.5 kg fat
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

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

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