1. 5-4 Dimensional Analysis Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 5-4 Dimensional Analysis Warm Up
Course 2
5-4
Dimensional Analysis
Warm Up
Use cross products to solve the proportions. 6 10 = 15 n 1.
n = 25 3 8 = r 64 2.
r = 24 9 17 = k 68 3.
k = 36 40 x = 30 9 4.
x = 12

3. 5-4 Dimensional Analysis Problem of the Day
Course 2
5-4
Dimensional Analysis
Problem of the Day
The sum of four consecutive integers is 182. What are the four numbers?
44, 45, 46, and 47

4. 5-4 Dimensional Analysis
Course 2
5-4
Dimensional Analysis
Learn to use dimensional analysis to make unit conversions.

5. Insert Lesson Title Here
Course 2
5-4
Dimensional Analysis
Insert Lesson Title Here
Vocabulary
unit conversion factor

6. 5-4 Dimensional Analysis
Course 2
5-4
Dimensional Analysis
You can use a unit conversion factor to change, or convert, measurements from one unit to another. A unit conversion factor is a fraction in which the numerator and denominator represent the same quantity, but in different units. The fraction below is a unit conversion factor that can be used to convert miles to feet. Notice that it can be simplified to one.
5,280 ft
1 mi =
= 1

7. 5-4 Dimensional Analysis
Course 2
5-4
Dimensional Analysis
Multiplying a quantity by a unit conversion factor changes only its units, not its value. The process of choosing an appropriate conversion factor is called dimensional analysis.

8. 5-4 Dimensional Analysis Helpful Hint
Course 2
5-4
Dimensional Analysis
When choosing a unit conversion factor, choose the one that cancels the units you want to change and replaces them with the units you want.
Helpful Hint

9. Additional Example 1: Making Unit Conversions
Course 2
5-4
Dimensional Analysis
Additional Example 1: Making Unit Conversions
An oil drum holds 55 gallons. How many quarts of oil will fill the drum? Use a unit conversion factor to convert the units.
One gallon equals 4 quarts so use the conversion factor or Choose the second one so the
1 gal
4 qt
gallon units will “cancel.” =
4 qt
1 gal
55 · 4 qt 1
55 gal ·
Multiply.
= 220 qt
220 quarts of oil will fill the drum.

10. 5-4 Dimensional Analysis Try This: Example 1
Course 2
5-4
Dimensional Analysis
Try This: Example 1
An ice cream recipe calls for 7 quarts of milk. How many pints of milk is this? Use a unit conversion factor to convert the units.
One quart equals 2 pints so use the conversion factor or Choose the second one so the
1 qt
2 pt
quarts units will “cancel.” =
2 pt
1 qt
7 · 2 pt 1
7 qt ·
Multiply.
= 14 pt
7 quarts of milk is 14 pints.

11. Additional Example 2A: Making Rate Conversions
Course 2
5-4
Dimensional Analysis
Additional Example 2A: Making Rate Conversions
Use a unit conversion factor to convert the units within each rate.
A. If orange juice sells for $1.28 per gallon,
what is the cost per ounce?
$1.28
gal
1 gal
4 qt
1 qt
32 oz =
$1.28 · 1 · 1
1 · 4 · 32 oz
Multiply. =
$1.28
128 oz
$1.28 per gallon is $0.01 per ounce. =
$1.28 ÷ 128
128 oz ÷ 128 =
$0.01
1 oz

12. Insert Lesson Title Here
Course 2
5-4
Dimensional Analysis
Insert Lesson Title Here
Additional Example 2B: Making Rate Conversions
Use a unit conversion factor to convert the units within each rate.
B. Convert 80 miles per hour to miles per minute.
80 mi
1 hr
1 hr
60 min =
80 mi · 1
1 · 60 min
Multiply. =
80 mi ÷ 60
60 min ÷ 60 ≈
1.33 mi
1 min
80 miles per hour is about 1.33 miles per minute.

13. 5-4 Dimensional Analysis Try This: Example 2A
Course 2
5-4
Dimensional Analysis
Try This: Example 2A
Use a unit conversion factor to convert the units within each rate.
If milk sells for $2.24 per gallon, what is the
cost per pint?
$2.24
gal
1 gal
4 qt
1 qt
2 pt =
$2.24 · 1 · 1
1 · 4 · 2 pt
Multiply. =
$2.24
8 pt
$2.24 per gallon is $0.28 per pint. =
$2.24
8 pt =
$0.28
1 pt

14. Insert Lesson Title Here
Course 2
5-4
Dimensional Analysis
Insert Lesson Title Here
Try This: Example 2B
Use a unit conversion factor to convert the units within each rate.
B. Convert 50 miles per hour to miles per minute.
50 mi
1 hr
1 hr
60 min =
50 mi · 1
1 · 60 min
Multiply. =
50 mi
60 min ≈
0.833 mi
1 min
50 miles per hour is about 0.83 miles per minute.

15. Additional Example 3: Measurement Application
Course 2
5-4
Dimensional Analysis
Additional Example 3: Measurement Application
The Mare Orientale crater on the Moon is more than 620 miles across. How many meters is this?
Use unit conversion factors that convert miles to
to kilometers, and then kilometers to meters. One
kilometer is equivalent to 0.62 mile.
1 km
0.62 mi
1,000 m
1 km =
620 · 1 · 1,000 m
0.62
620 mi · =
620,000 m ÷ 0.62
0.62 ÷ 0.62 =
1,000,000 m
620 miles is 1,000,000 meters.

16. 5-4 Dimensional Analysis Try This: Example 3
Course 2
5-4
Dimensional Analysis
Try This: Example 3
Mary went to the grocery store to buy 5 pounds of peaches. How many grams is this?
Use unit conversion factors that convert pounds to
to kilograms, and then kilograms to grams. One
kilogram is equivalent to 2.2 pounds.
1 kg
2.2 lb
1,000 g
1 kg =
5 · 1 · 1,000 g
2.2
5 lb · =
5,000 g ÷ 2.2
2.2 ÷ 2.2
≈ 2,273 g
5 pounds is about 2,273 grams.

17. Insert Lesson Title Here
Course 2
5-4
Dimensional Analysis
Insert Lesson Title Here
Lesson Quiz
Use a unit conversion factor to convert the units.
1. Football fields are 100 yards long. How many feet
is that?
300 feet
2. In biology lab you measure a grasshopper’s wing
span to be 3 inches long. How many centimeters is this?
7.62 cm
Use a unit conversion factor to convert the units
within a rate.
3. On a freeway a car’s speed is 62 miles per hour.
What speed is that in feet per hour?
327,360 ft/h
4. If you are paid $7.50 per hour to watch your
neighbor’s children, how much are you paid per
minute?
12.5 cents per minute