1. Dimensional Analysis
DHS Chemistry ferrer

2. Setting Up Ratios 100 centimeters = 1 meter can be written as
100 cm OR m___
1 m cm
8 slices = 1 pizza can be written as
1 pizza OR slices___
8 slices pizza

3. The Format # x # x # x # = 1 # # # OR # # # = 1 # #
# # # OR
# # # =
# #
Note: Unless you are using 1 as a spot filler, all numbers should ALWAYS include units

4. Understanding order of operations & typing in calculator keys correctly
Solve =
Method 1: 10 X 13 X 6 = then divide x 4 = 8
Method 2: 10 X 13 X 6 / 2 / 4 =
Method 3: 10 X 13 / 2 X 6 / 4 =

5. Try It =
0.308

6. Canceling out units
Just as numbers are multiplied and divided, units are too. Cancel out all units that are located in both the numerator and denominator to reveal the left over units.
cm in feet yard = yard cm in feet

7. Try It
week day hr min sec = sec
1 week day hr min

8. Putting the numbers & units together
3 weeks 7 day hr 60 min 60 sec =
week 1 day hr 1 min
= sec
Rules?

9. I. One-Step Conversions

10. I. One- Step Conversions EX 1: Determine the number of slices in 282
I. One- Step Conversions EX 1: Determine the number of slices in pizzas
Step 1) what are you given?
Step 2) What are you trying to get?
Step 3) List your relationships
(remember from pg 1 of the notes)
Step 4) Set up your problem
282.3 pizzas
Number of slices
1 pizza = 8 slices
282.3 pizzas
8 slices
=2258.4
slices 1
1 pizza

11. EX 2: Determine the number of dozen eggs in 3.8 x 103 eggs.
Step 1) what are you given? 3.8 X 103 eggs
Step 2) What are you trying to get? Dozen eggs
Step 3) List your relationships
12 eggs = 1 dozen
Step 4) Set up your problem
These should match
3.8 X 103 eggs
1 dozen
=317
Dozen of eggs 1
12 eggs

12. Practice Relationship 1 foot = 12 inches 2821 in 1 foot = 235 feet 1
Determine the number of feet in 2821 inches.
Relationship 1 foot = 12 inches
want
given
Start with what’s given
2821 in
1 foot
= 235
feet 1
12 in

13. Practice Relationship 1000g = 1kg 0.03455 kg 1000 g = 34.6 g 1 1 kg
2. Determine the number of g in kg
Relationship 1000g = 1kg
want
given
Start with what’s given kg
1000 g
= 34.6 g 1
1 kg

14. Relationships 1 mi = 1609.3 meter
given
want
Relationships 1 mi = meter
1 mi = km
Start with what’s given
37 mi km
= 59.5 km 1
1 mi
99 mi km
= 159 km 1
1 mi

15. Solving the same problem, but in a different way

16. Relationships 1 mi = 1609.3 meter
given
want
Relationships 1 mi = meter
1 km = 1000 m
Start with what’s given
37 mi m
1 km
= 59.5 km 1
1 mi
1000 m

17. For every problem, start with:
Given:
Want:
Relationships:

18. II. Multi-Step Conversions

19. Given: Want: Relationships: Ex. 1 Convert 0.115 km to cm 0.115 km
100 cm = 1 m
1 km = 1000 m

20. Ex. 1 Convert 0.115 km to cm Relationships 1km = 1000m 100cm = 1m
given
want
Start with what’s given
0.115 km
1000 m
100 cm 1
1 km
1 m cm
= 1.15 x 104

21. Given: Want: Relationships: Ex. 2 Convert 323 mL to cups 323 mL
1000 mL = 1 L
1 L = 1.06 quarts
1 quart = 4 cups

22. Ex. 2 Convert 323 mL to cups Relationships 1000 mL = 1L 4 cups 323 mL
1L = 1.06 quarts
1 quart = 4 cups
given
want
Start with what’s given
4 cups
323 mL
1 L
1.06 qt. 1
1000 mL
1 L
1 qt.
= 1.37
cups

23. Practice 1: Convert 7.005 ft to mm
Given:
Want:
Relationships:
7.005 ft
____ mm
1 foot = 12 inches
1 inch = 2.54 cm
100cm = 1 m
1m = 1000mm

24. Practice 1: Convert 7.005 ft to mm
Relationships 1 foot = 12 inches
2.54cm = 1 in
100 cm = 1 m
1 m = 1000 mm
given
want
Start with what’s given
Use this slide as a template for others
7.005 ft
12 in
2.54 cm
1 m
1000 mm 1
1 ft
1 in
100 cm
1 m
= 2135 mm

25. Practice 2: calculate the number of seconds in 2 years
Given:
Want:
Relationships:
2 years
____ seconds
1 year = days
24hrs = 1 day
60 min = 1 hr
1 min = 60 sec

26. Practice 2: calculate the number of seconds in 2 years
Relationships 1 year = days
1 day = 24 hours
1 hr = 60 min
1 min = 60 sec
given
want
Start with what’s given
Use this slide as a template for others
60 sec
2 years
24 hrs
60 min
days 1
1 year
1 day
1 hr
1 min
= 6.31 X 10 7
seconds

27. What does that price mean?
$1.99 = 1lb

28. III. Combination Unit Conversions

29. Writing Clean Fractions
Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem.
36.0 m/s 36.0 m OR s ___
s m
722 mi/hr mi OR hr__
hr mi

30. Writing clean fractions from the denominator
Remember from algebra, that a fraction in the denominator can be multiplied by its reciprocal. Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem.
52m to m s = s m/s m
46mi to mi hr = hr mi/h mi

31. EX 1: Convert 0.083 km/hr to m/s
Given:
Want:
Relationships:
0.083 km/hr
____ m/s
1 km = 1000m
1 hr = 60 min
1 min = 60 sec

32. EX 1: Convert 0.083 km/h to m/s 0.083km 1000m 1 hr 1 min 1hr 1 km
Relationships 1km = 1000m
1h = 60 min
1 min = 60 s
given
want
Start with what’s given
Use this slide as a template for others
0.083km
1000m
1 hr
1 min
1hr
1 km
60 min
60 s
m/s
= 2.31 X 10-2

33. EX 2: Convert 2.85 g/mL to lb/gal
Given:
Want:
Relationships:
2.85 g/mL
____ lbs/gal
454g = 1lbs
1 gal = 4 quarts
1.06 qts = 1L
1 L = 1000mL

34. EX 2: Convert 2.85 g/mL to lb/gal
Relationships 454 g = 1lb
1000mL = 1 L
1.06qt = 1 L
4 qt = 1 gal
given
want
Start with what’s given
Use this slide as a template for others
1 L
4 qt
2.85 g
1lb
1000mL
1mL
1 L
454 g
1.06 qt
1 gal
= 23.7
lb/gal

35. Given: Want: Relationships: 3.56 cm/s ____ ft/hr 1 ft = 12 in
1. Convert 3.56 cm/s to ft/hr
Given:
Want:
Relationships:
3.56 cm/s
____ ft/hr
1 ft = 12 in
2.54 cm = 1 in
1 hr = 60 min
1 min = 60 sec

36. 3.56 cm 1 in 1 ft 60 s 60 min 1 s 2.54 cm 12 in 1 min 1 hr = 420 ft/hr
1. Convert 3.56 cm/s to ft/h
Relationships cm = 1 in
12 in = 1 ft
60 s = 1 min
1 hr = 60 min
want
given
Start with what’s given
Use this slide as a template for others
3.56 cm
1 in
1 ft
60 s
60 min
1 s
2.54 cm
12 in
1 min
1 hr
= 420
ft/hr

37. 2. Convert $25.00/feet to cents/cm
Given:
Want:
Relationships:
$25.00/ft
____ cents/cm
$1.00 = 100 cents
1 ft = 12 inches
2.54 cm = 1 in

38. 2. Convert $25.00/feet to cents/cm
Relationships $1 = 100 cents
2.54 cm = 1 in
12 in = 1 ft
given
want
Start with what’s given
Use this slide as a template for others
1 in
$ 25.00
100 cents
1 ft
1 ft
12 in $1
2.54 cm
= 82.0
cents/cm

39. Solving Word Problems using Dimensional Analysis

40. If you are given multiple numbers in a problem, only one number will be your starting point. The other numbers are relationships that you will use in your problem. If you are given multiple numbers and one of them involves a “/” (e.g. m/s), then always use the “/” as a relationship and start with the other number.

41. If it helps, change any combination unit into a relationship ex
If it helps, change any combination unit into a relationship ex. 0.05mL/s 0.05mL = 1 s

42. Given: Want: Relationships: 0.05mL/s 1 day ____ Liters 0.05mL = 1 sec
EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be lost in 1 day?
Given:
Want:
Relationships:
0.05mL/s
1 day
____ Liters
0.05mL = 1 sec
1000mL = 1 L
60 sec = 1 min
1 day = 24 hr
1 hr = 60 min

43. 1 L 1 day 24 hr 60 min 60 s 0.05 mL 1 1 hr 1000 mL 1 day 1 min 1 s
Relationship
EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be lost in 1 day?
want
given
Relationships mL = 1 s 60 min = 1 hr
1000mL = 1 L 24 hr = 1 day
60s = 1 min
Start with what’s given
Use this slide as a template for others
1 L
1 day
24 hr
60 min
60 s
0.05 mL 1
1 hr
1000 mL
1 day
1 min
1 s
= 4.32 L

44. Finally, note dimensional analysis can be used anytime you can say something is equal to something else. It does not have to involve standard conversion factors.

45. Given: Want: Relationships: 2.5 hours ____ feet 24 frames = 1 sec
EX 1: Motion pictures are shown at a speed of 24 frames, or individual pictures, each second. If a standard frame is 1.9 cm long, how long will the strand of film be (in ft) for a 2 ½ hr movie?
Given:
Want:
Relationships:
2.5 hours
____ feet
24 frames = 1 sec
1 hr = 60 min
1 in = 2.54cm
1 frame = 1.9cm
1 min = 60 sec
1 ft = 12 in

46. 2.5 hr 60 min 60 s 24 frames 1in 1 ft 1 1 min 1 hr 1 s 12 in 1 frame
EX 1: Motion pictures are shown at a speed of 24 frames, or individual pictures, each second. If a standard frame is 1.9 cm long, how long will the strand of film be (in feet) for a 2 ½ hour movie?
Relationship
relationship
want
want
given
Relationships 24 frames = 1 s 1 frame = 1.9cm
1 hr = 60 min 60 s = 1 min
1in = 2.54 cm 1 ft = 12 in
Use this slide as a template for others
Start with what’s given
2.5 hr
60 min
60 s
24 frames
1.9 cm
1in
1 ft 1
1 min
1 hr
1 s
12 in
1 frame
2.54 cm = ft

47. Given: Want: Relationships: 10 gallons ____ trips 60 mi = 1 gal
1. The Toyota Prius gets 60 mi/gal of gas. If each trip to school is 3.5 km, how many trips can I make with 10 gallons of gas?
Given:
Want:
Relationships:
10 gallons
____ trips
60 mi = 1 gal
1 trip = 3.5km
1000m = 1km
1 mile = m

48. 10gal 60 mi 1609.3 m 1 km 1 trip 1 1 mi 1 gal 1000m 3.5 km = 276 trips
1. The Toyota Prius gets 60 mi/gal of gas. If each trip to school is 3.5 km, how many trips can I make with 10 gallons of gas?
Relationship
relationship
want
given
Relationships 60 miles = 1 gal 1 trip = 3.5 km
1 mi = m 1000m = 1km
Start with what’s given
10gal
60 mi m
1 km
1 trip
Use this slide as a template for others 1
1 mi
1 gal
1000m
3.5 km
= 276
trips

49. Given: Want: Relationships: 1 day ____ kg 1 sec = 2500g 1kg = 1000g
2. Every second 2500 g of sulfuric acid flows out of a pipe. How many kg of sulfuric acid will flow in 1 day?
Given:
Want:
Relationships:
1 day
____ kg
1 sec = 2500g
1kg = 1000g
60 s = 1 min
60 min = 1 hr
24 hrs = 1 day

50. 1 day 24 hr 60 min 60 s 2500g 1 kg 1 1 hr 1 day 1 min 1 s 1000g
2. Every second 2500 g of sulfuric acid flows out of a pipe. How many kg of sulfuric acid will flow in 1 day?
Relationship
want
given
Relationships 1 s = 2500g 60s = 1 min
1000g = 1kg 60 min = 1 hr
24 hr = 1 day
Start with what’s given
1 day
24 hr
60 min
60 s
2500g
1 kg
Use this slide as a template for others 1
1 hr
1 day
1 min
1 s
1000g = kg

51. Tips for studying
Try doing the review without using the conversion sheet
Quiz yourself with the conversions
Do extra practice problems (your textbook may have some)