1. Dimensional Analysis

2. What is Dimensional Analysis?
Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value.
It is used to go from one unit to another.

3. Organized method of problem-solving
Used in chemistry, physics, engineering, and medicine
Communicates the path to scientists that follow your work
Records your own path for your future use

4. How Does Dimensional Analysis Work?
A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.

5. You are not changing the size, just the name.
CONVERSIONS
You are not changing the size, just the name.

6. Examples of Conversions
60 s = 1 min
60 min = 1 h
24 h = 1 day

7. Fill in the Missing Numbers12
1 foot = _____ inches
1 meter = _____ centimeters
1 pound = _______ ounces
1 minute = ______ seconds
1 hour = ________ minutes
1 day = __________ seconds
100 16 60 60
What is the purpose of knowing these facts? Give me some examples.
86,400

8. Unit conversion factor
A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.
1 ft
? in.
1 yd
? ft
1 mi
1lb
? oz
1 pt
? c
1 qt
? pt
1 gal
? qt
1 hr
? min
1 min
? s 1m
? cm
1km
? m
Fill in the blanks for as many as you know. Compare with your neighbor.

9. Unit conversion factor
A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.
Ask for some reciprocals so you know they understand.

10. Choose a unit conversion factor that…
Introduces the unit you want in the answer
Cancels out the original unit so that the one you want is all that is left.

11. “Canceling” out Words

12. Examples of Conversions
You can write any conversion as a fraction.
Be careful how you write that fraction.
For example, you can write
60 s = 1 min
as 60s or 1 min
1 min s

13. Examples of Conversions
Again, just be careful how you write the fraction.
The fraction must be written so that like units cancel.

14. Practice: Choose the appropriate conversion factor.
Inches to feet
Minutes to hours
Meters to centimeters

15. Use the one that will cancel out the units you want to change
Convert 8 yards to feet…
Make a decision: What conversion factor will you use?
Set up the problem: Multiply the measurement by the conversion factor.
Hint!
Use the one that will cancel out the units you want to change
Solve the problem: Perform the multiplication

16. A bucket holds 16 quarts. How many gallons of water will fill the bucket? Use a unit conversion factor to convert the units.
What are the two conversion factors comparing quarts and gallons?
Which one will “cancel” quarts?
16 qt 

17. You Try it!
One bag of apples weighs 64 ounces. How many pounds does it weigh?
Darren drank 2 liters of water. How many milliliters of water did he drink?

18. Steps Start with the given value. Don’t forget the units!!!!
Draw the chart.
Write the multiplication symbol.
Choose the appropriate conversion factor.
Multiply the numbers & cancel the units. Remember, cancel like units.
Reduce the fraction (if needed).
Count significant figures and round to the appropriate number.

19. Let’s try some examples together…
Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas?
Given: 7 pizzas
Want: # of slices in 7 pizzas
Conversion: 12 slices = one pizza

20. conversion 7 pizzas 12 slices = 84 slices 1 pizza
Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas?
conversion
Starting amount
End Amount
7 pizzas
12 slices
= 84 slices
1 pizza

21. Let’s try some examples together…
2. How old are you in days?
Given: 15 years
Want: # of days old
Conversion: 365 days = one year

22. conversion 15 years 365 days = 5475 days 1 year
How old are you in days?
conversion
Starting amount
End Amount
15 years
365 days
= 5475 days
1 year

23. Let’s try some examples together…
3. There are 2.54 cm in one inch. How many inches are in 17.3 cm?
Given: 17.3 cm
Want: # of inches
Conversion: 2.54 cm = one inch

24. There are 2.54 cm in one inch. How many inches are in 17.3 cm?
conversion
Starting amount
End Amount
17.3 inches
2.54 cm
= 43.9 cm
1 inch

25. Now, you try… Determine the number of eggs in 23 dozen eggs.
If one package of gum has 10 pieces, how many pieces are in packages of gum?

26. Multiple-Step Problems
Most problems are not simple one-step solutions. Sometimes, you will have to perform multiple conversions.
Example: How old are you in hours?
Given: 17 years
Want: # of days
Conversion #1: 365 days = one year
Conversion #2: 24 hours = one day

27. How old are you in hours? = 131,400 hours 15 years year 365 days
Starting amount
conversion
conversion
End Amount
15 years
365 days
24 hours
= 131,400 hours
year
1 day

28. Combination Units
Dimensional Analysis can also be used for combination units.
Like converting km/h into cm/s.
Write the fraction in a “clean” manner:
km/h becomes km h

29. Combination Units Example: Convert 0.083 km/h into m/s.
Given: km/h
Want: # m/s
Conversion #1: 1000 m = 1 km
Conversion #2: 1 hour = 60 minutes
Conversion #3: 1 minute = 60 seconds

30. Convert 0.083 km/h into m/s 0.083 km hour = 0.023 m s 1000 m 1 km
reduce
Starting amount
conversion
conversion
multiply
End Amount
0.083 km hour
1000 m 1 km
1 hour 3600 s
83 km 3600 s
= m s