1. General Chemsitry Dimensional Analysis Method
Follow along on your Dimensional Analysis Worksheet and do the example problem with the presentation

2. Answer = 5 Which is bigger? 120 Pennies 5 Quarters 21 Nickels
The units are more important than the numbers!

3. A physical quantity must include:
Number
+ Unit

4. Conversions
Often, it is necessary to change one unit into another. A conversion factor is needed:
A conversion factor is a fraction (ratio) representing a relationship between two units. For Example:
Equivalence
statement
Conversion factor

5. 2.70 g = 1 mL 2.70 g = 1.00 mL 1 gallon = 3.79 L 2.54 cm = 1 inch
The density of aluminum is 2.70 g/mL. What does this mean?
How many significant figures are in 2.70 g and 1 mL?
A rule of thumb for conversion factors that have decimal values: They are not unlimited and you need to look at the number of sig figs
Examples:
2.70 g = 1 mL
2.70 g = 1.00 mL
3 sig figs
3 sig figs
1 gallon = 3.79 L
3 sig figs
3 sig
figs
4 sig
figs
2.54 cm = 1 inch
1 m =39.37 inches

6. What is Dimensional Analysis?
Dimension – means Unit
Analysis – means Problem Solving
Math using units!
Use the units to find the solution to a problem!

7. Setup 1. Write down given 2. Set up workspace
Write down units of answer
→Start with your given unit and solve until you reach your desired unit!
→Remember: If the unit is the same on top and bottom it will cancel.

8. Example: How many inches are in 13.5 feet? →What is given? 13.5 Feet
→What is desired unit? inches
→What conversion factor do we know? 12 inches = 1 foot
13.5 feet
12 inches
Solution: =
inches
1 foot

9. To Calculate: = 12 inches 13.5 feet inches 1 foot 162 inches
→ Everything on top is multiplied and everything on the bottom is divided.
→ Plug the numbers in the calculator and let it do all the work!
13.5 feet 12
inches =
inches 1
foot
162 inches
Why 3 sig figs?

10. Multi-step problems
given unit #2 unit desired unit
given unit #2 unit
= desired unit
Example : How many cm are in 4.75 feet?
(12 inches = 1 foot) and (2.54 cm = 1 in) *This would be #2
4.75 ft 12
2.54 cm
inches =
145 cm 1 ft 1
inch
(4.75 x 12 x 2.54)
(1 x 1)

11. Multi-step, cont. = Example 7: How many seconds are in 2.5 weeks?
2.5 wks 7
days 24
hours 60
min 60 s = s 1 1
wks 1
days
hours 1
min s

12. Know these prefixes for the quiz!
Metric Prefixes
Know these prefixes for the quiz!
Prefix
Symbol
Meaning
kilo- k
hecto- h
deca- da
deci- d
centi- c
milli- m
1000
1 km = m
100
1 hm = 100 m 10
1 dam = 10 m
0.1
10 dm = 1 m
0.01
100 cm = 1 m
0.001
1000 mm = 1 m

13. Metric Conversions kilo- hecto deca- base unit deci- centi- milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
/ / /1000

14. = Example : How many centigrams (cg) are in 5 g? 5 g 100 cg 500 cg 1 g2
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
Example :
How many centigrams (cg) are in 5 g?
There are 102 or 100 cg in a g.
5 g
100 cg =
500 cg 1 g

15. = Example : How many kilometers (km) are in 12 meters m? 12 m 1 km3 2 1
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
Example :
How many kilometers (km) are in 12 meters m?
There are 103 or 1000 m in 1 km.
12 m 1 km =
0.012 km
1000 m

16. Class Practice
Convert the following with the dimensional analysis method:
Example 4:
0.015 m = ______ mm
Example 5:
0.34 dg = _______ g
0.015 m
1000 mm = 15 mm 1 m
0.34 dg 1 g =
0.034 g 10 dg

17. Two step metric conversions (prefix unit to a prefix unit)
Example :
A pencil is 17.8 cm long. What is its length in km?
17.8 cm 1 m 1 km = km
100 cm
1000 m

19. Square and Cubic U nit Conversions
Measured dimensions of a rectangle:
length (L) = 9.70 cm
width (W) = 4.25 cm L W
Find area of rectangle.
A = L . W
= (9.70 cm)(4.25 cm) =
41.2 cm 2
. cm

20. Example 9: Convert 41.2 cm2 to m2.=
0.412 m2
WRONG! =
0.412 cm.m
Recall that… 41.2 cm2 = 41.2 cm.cm
41.2 cm.cm
100 cm
1 m
100 cm
1 m = m2 m2

21. Square and cubic unit conversions
Example 10: How many m3 are in 3 cm3?
cm.cm.cm
100 cm
1 m 3 cm 3 2
100 cm
1 m
100 cm
1 m = m3 m3
3 x 10-6 m3 or

22. Complex Units (the hidden equality)
What does 60 mi/hr (this is a complex unit) really mean?
60 miles = 1 hr or

23. Complex Units a. Using as a conversion factor
Example 11:
The density of gold is 19.3 g/mL. What is the mass if the
volume is L?
19.3 g = 1 mL
244.8 L
1000 mL
19.3 g =
 106 g 1 L 1 mL
4.72  106 g

24. Used as a Complex Units b. Using as a given
Example 12:
The density of gold is 19.3 g/mL, what is it in cg/kL?
19.3 g = 1 mL
19.3 g
100 cg
1000 mL
1000 L cg kL =
1.93  109
1 mL 1 g 1 L 1 kL