1. Dimensional Analysis and scientific notation

2. What is Dimensional Analysis?
Dimensional analysis is the skill of converting from one unit to another.
Converting within the metric system is easy but if we are want to know how many inches (English system) are in a kilometer (metric system) things get a little more complicated.

3. A conversion factor is 2 units that are equal to each other.
Picket fence method
In order to use this method we have to know our conversion factors.
A conversion factor is 2 units that are equal to each other.
Conversion factors:
1 inch is equal to 2.54 cm
12 inches is equal to 1 foot
60 minutes is equal to 1 hour

4. What are some other conversion factors?
Days and week?
Hours and day?
Feet and mile?

5. How to…
Step 1 – Find your starting number and unit
Step 2 – set up a picket fence
Step 3 – fill in the fence with your starting number/unit and conversion factor
Step 4 – cancel out like units
Step 5 – multiply across the top and bottom
Step 6 – solution

6. How many seconds are in 47 minutes? Step 1: starting number and unit
Step 2: set up your fence
Step 3: fill in the fence with your conversion factor
Step 4: cancel like units
Step 5: multiply across the top and bottom
Step 6: solution
47 min
60 sec
2820 sec
2,820 seconds in 47 minutes
1 min 1

7. The problem: How many centimeters are in 9 inches?
Step 1 – Find your starting number and unit: inches
Step 2 – set up a picket fence:
Step 3 – fill in the fence with your starting number/unit and conversion factor:
Step 4 – cancel out like units
Step 5 – multiply across the top and bottom
Step 6 – solution cm are in 9 inches
9 in
2.54 cm
1 in
22.68 cm 1

8. Sometimes you will have to use more than one conversion factor.
For example if we were going to find out how many seconds there were in 1 year.
The steps are the same we just need to expand the picket fence and make sure we’ve got all of the conversion factors.

9. Conversion factors:
1 year = 365 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

10. 1 yr
365 days
24 hrs
60 min
60 sec
1 yr
1 day
1 hour
1 minute
= 31,536,000 seconds

11. Practice
Conversion Factors
365 days = 1 year lbs = 1 ton
1 mile = 5280 feet 4 cups = 1 qt.
28.35 g = 1 oz gal = 3.78 L
4 qts = 1 gal 1 lb = 16 oz.
Convert 16 years to days.
How many feet are in 2.3 miles?
Convert 4 tons to grams.
Convert 400 cups to Liters.

12. Scientific Notation
An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about centimeters across.
The length of these numbers in standard notation makes them awkward to work with.
Scientific notation is a shorthand way of writing such numbers.

13. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer

14. 20,000,000,000,000,000,000,000 atoms in a penny.
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
After the 2.

15. 20,000,000,000,000,000,000,000.
How many place values did you move the decimal? 22

16. When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.0 x 1022

17. The average size of an atom is about 0.00000003 centimeters across.
Where would the decimal go to make the number be between 1 and 10?
After the 3
The decimal was moved how many places? 8
When the original number is less than 1, the exponent is negative.
3.0 x 10–8

18. In scientific notation the number of atoms in a penny is 2
In scientific notation the number of atoms in a penny is 2.0 x 1022, and the size of each atom is 3.0 x 10–8 centimeters across.

19. Practice
Write 28,750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

20. Practice
Write in scientific notation.
.36 x 10-7
36.0 x 109
3.6 x 108
3.6 x 10-8

21. Express 1.8 x 10-4 in standard notation.
HINT: The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

22. Practice
Express 4.58 x 106 in standard notation.
458,000,000
4,580,000

23. Express 3.9 x 10-11 in standard notation.
3,900,000,000,000
39,000,000,000