1. Scientific Notation and Factor Label Method
Lesson 2
January 20th, 2011
Scientific Notation and Factor Label Method

2. Scientific Notation
Dealing with larger numbers can be difficult. We like to deal with small numbers.
Ex kg
= 0.895mg
If we cannot change the units we can use scientific notation. It allows us to manage large numbers without changing the units

3. Scientific Notation
Scientific notation allows us to write numbers in the form of
a x 10n
Where 1 < |a| <10 and all the digits in the coefficient are significant
Example million kilometres
= km
Or = x 108 km

4. Scientific Notation How do I find n? Count the decimal places
units
If 2 is the number out in the front, the rest of the numbers must be behind the decimal place. Count from the right how many times the decimal place would have to move to make it 2.3
n= 11
2.3 x units

5. Scientific Notation Bring out your calculators
Look for a key that says
EXP Or EE
This key allows you to just type in the start and it fills in the “x 10”. Then you just add the exponent.
Try it out. Type in 1.5 EXP 5 =
It should say

6. Scientific Notation Practice
Decimal Notation
Scientific Notation
127
1.27 x 102
0.0907
9.07 x 10 – 2
5.06 x 10 – 4
2.3 x 1012
Decimal Notation
Scientific Notation
127
1.27 x 102
0.0907
9.07 x 10 – 2
5.06 x 10 – 4
2.3 x 1012
Decimal Notation
Scientific Notation
127
1.27 x 102
0.0907
5.06 x 10 – 4
2.3 x 1012
Decimal Notation
Scientific Notation
127
0.0907
5.06 x 10 – 4
2.3 x 1012
Decimal Notation
Scientific Notation
127
1.27 x 102
0.0907
9.07 x 10 – 2
5.06 x 10 – 4
2.3 x 1012

7. Factor Label Method

8. The factor label method
Used to convert between units
km to miles, m to km, mol to g, g to mol, etc.
To use this we need:
Desired quantity,
Given quantity,
Conversion factors
Conversion factors are valid relationships or equities expressed as a fraction

9. E.g. for 1 km=0.6 miles the conversion factor is

10. Q. write conversion factors for 1 foot =12 inches
Q. what conversion factors can you think of that involve meters?

11. Conversion factors
Conversion factors for 1 ft = 12 in
There are almost an infinite number of conversion factors that include meters:

12. Conversion Factor Steps
1.Write down the desired quantity/units
2.Equate the desired quantity to given quantity
3.Determine what conversion factors you can use (both universal and question specific)
4.Multiply given quantity by the appropriate conversion factors to eliminate units you don’t want and leave units you do want
5.Complete the math

13. First write down the desired quantity
example
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
First write down the desired quantity

14. Next, equate desired quantity to the given quantity
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
Next, equate desired quantity to the given quantity

15. Now we have to choose a conversion factor
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
Now we have to choose a conversion factor

16. What conversion factors are possible?
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
1 km
0.621 mi
0.621 mi
1 km
What conversion factors are possible?

17. Pick the one that will allow you to cancel out miles
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

18. Pick the one that will allow you to cancel out miles
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

19. Multiply given quantity by chosen conversion factor
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
# km
= 47 mi
1 km
0.621 mi
0.621 mi
1 km
Multiply given quantity by chosen conversion factor

20. Multiply given quantity by chosen conversion factor
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621 mi
# km
= 47 mi
Multiply given quantity by chosen conversion factor

21. Cross out common factors
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621 mi
# km
= 47 mi
Cross out common factors

22. Cross out common factors
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47
Cross out common factors

23. Are the units now correct?
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47
Are the units now correct?

24. Yes. Both sides have km as units.
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47
Yes. Both sides have km as units.

25. Yes. Both sides have km as units.
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47
Yes. Both sides have km as units.

26. Now finish the math. x 1 km 0.621 = 75.7 km # km = 47
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
= 75.7 km
# km
= 47
Now finish the math.

27. The final answer is 75.7 km x 1 km 0.621 = 75.7 km # km = 47
Q - How many kilometers are in 47 miles? (note: 1 km = miles)
x 1 km
0.621
= 75.7 km
# km
= 47
The final answer is 75.7 km

28. Summary The previous problem was not that hard
In other words, you probably could have done it faster using a different method
However, for harder problems the factor label method is easiest

29. Rearranging Equations

30. Rules to rearranging equations
RULE #1: you can add, subtract, multiply and divide by anything, as long as you do the same thing to both sides of the equals sign. 
In an equation, the equals sign acts like the fulcrum of a balance: if you add 5 of something to one side of the balance, you have to add the same amount to the other side to keep the balance steady

31. Rule 1 example Find b in the equation y = mx + b
Subract mx from each side of the equation
Y – mx = mx – mx + b
Y – mx = b

32. RULE #2: to move or cancel a quantity or variable on one side of the equation, perform the "opposite" operation with it on both sides of the equation. 
For example if you had g-1=w and wanted to isolate g, add 1 to both sides (g-1+1 = w+1). Simplify (because (-1+1)=0) and end up with g = w+1. 

33. More complex example
This equation is used to calculate the density of icebergs
We will isolate ρobject which is the density of the iceberg itself.

34. Start by isolating the equation in brackets
Divide both sides by Htotal =

35. Next we will isolate the faction that contains ρobject
Subtract 1 on each side =

36. Multiply both sides by ρfluid to get rid of the fraction
Cancel out ρfluid

37. We will now remove the negative sign by multiplying by -1=

38. Rearrange the equation a little
And we are done