1. Performing these conversions is a lot like going on a road trip.
Dimensional Analysis
Performing these conversions is a lot like going on a road trip.

2. MATH IS THE
LANGUAGE OF
CHEMISTRY!!!

3. Scientific Notation
Scientist use special notation to express very large or very small numbers.
Example I: 300,000,000 g can be written as…
3 x 108 g
Ex II: 1,007,000,000 sec can be written as…
1.007 x 109 sec
Ex III: mL can be written as…
4.76 x mL

4. Significant Figures Atlantic - Pacific Rule:
Decimal Present: Count from the Pacific side
Decimal Absent: Count from the Atlantic side
Start counting at the first non-zero number and count until you reach the end of the number
Ex. I:
Decimal Present… Pacific (left)… 6 sig. figs.
Ex. II: 300,700
Decimal Absent… Atlantic (right)… 4 sig. figs.

5. Before we take this trip, let’s review significant figures…
Determine how many significant figures are in each of the following measurements.
L ___________
m ___________
g ___________
47,900 mm ___________
7,000,000,001 miles ___________
8.07 Hz ___________ 5 5 5 3 10 3

6. More practice… 366.2 L ___________ 366 L 9,047,022 mg ___________
Round the following measurements off so that they each contain 3 significant figures.
366.2 L ___________
9,047,022 mg ___________
12.76 g ___________
999.9 J ___________
366 L
9,050,000 mg
12.8 g
1.00 x 103 J
Notice this one must be in scientific notation to have 3 sig. figs.

7. Significant Figures in Calculations
When multiplying and dividing, limit and round to the least number of significant figures in any of the factors.
Example:
23.0 x 432 x 19 = 188,784 = 190,000
The answer is expressed as 190,000 or 1.9 x 105 since 19 has only two sig. figs.

8. Significant Figures in Calculations
When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers involved in the calculation.
Example:
= = 255.5
The answer is expressed as since 46.0 has only one decimal place.

9. Before we take this trip, let’s review significant figures…
Perform the prescribed operations. Round your answers to the proper # of sig. figs.
36.57 m / 3.21 s = ___________
41.376g g g=___________
5.67 m x m ___________
(5.83 m/ 2.67 s) /2.1 s ___________
9.374 V x 6 ___________
11.4 m/s
97.6 g
76.2 m2
1.0 m/s2
60 V
From now on, we will round all our answers to the correct # of significant figures.

10. Let’s say you want to travel from Oracle Jct to Casa Grande...
Now back to our road trip…
Let’s say you want to travel from Oracle Jct to Casa Grande...
You must travel through Tucson… a two part trip.

11. Rule: You must stay on the roads

12. X

13. Rule: You need a map. Sometimes the map can be in your head
Rule: You need a map. Sometimes the map can be in your head. But, not at first.

14. OK…Lets talk about making maps and solving conversion problems
OK…Lets talk about making maps and solving conversion problems. The method we use is called the “Factor-Label” method, a.k.a. dimensional analysis.

15. For Example: Given 1 kildurkin = 18 gallons
kildurkins
gallons
This is our map.

16. =0.78 kildurkins 14 gallons 1 kildurkins 18 gallons
For Example: Given 1 kildurkin = 18 gallons
kildurkins
gallons
How many kildurkins is 14 gallons?
14 gallons
1 kildurkins
=0.78 kildurkins
18 gallons

17. General Format...
given
going to
coming from

18. Let’s expand the map...
Also given: 2 farkins = 1 kildurkin
kildurkins
farkins
gallons

19. Also given: 1 hogshead = 63 gallons
1 barrel = 3.3 bushels
hogshead
1 bushel = 8 gallons
kildurkins
farkins
gallons
barrel
bushel

20. Now, Lets solve a problem.
How many hogsheads are 14 barrels?
Finish Here
hogshead
The trip will require 3 transitions 3
kildurkins
farkins
gallons 2
barrel
bushel
Given: Start Here 1

21. = 5.9 hogsheads How many hogsheads are 14 barrels? hogshead Given 3
gallons
14 barrels
3.3 bushels
8 gallons
1 hogshead
63 gallons
1 barrel
1 bushel 2
= 5.9 hogsheads
barrel
bushel 1

22. Now you try one. How many farkins is 3.00 bushels?
End Here
hogshead
kildurkins
farkins
gallons
Start Here
barrel
bushel
This will require 3 Conversions.

23. = 2.67 farkins bushels gallons kildurkins farkins 3.00 bushels

24. Wow! How Cool Is That!