1. Scientific Notation Dimensional Analysis
Analyzing Data Part 2
Scientific Notation
Dimensional Analysis

2. Scientific Notation
Scientific Notation can be used to express any number as a number between 1 and 10 (known as the coefficient) multiplied by 10 and raised to a power (an exponent)
Coeffiecient Exponent
2.0 X 10 3
BUT WHY DO WE USE IT?

3. Scientific Notation
The Hope Diamond is carats and about 1 inch wide.
It contains about 460,000,000,000,000,000,000,000 atoms. One of those 460,000,000,000,000,000,000,000 atoms weighs about grams.
1. How many sig figs do you
count in both numbers?
2. Would you want to write
these numbers, over and over
again?

4. Scientific Notation
Luckily we can write these numbers in a more useful way.
Take 460,000,000,000,000,000,000,000 for example. To write this in scientific notation, I need to follow a few steps.

5. 460,000,000,000,000,000,000,000
1. Find where the decimal is. If there is no decimal, place it at the end of the number.
460,000,000,000,000,000,000,000.

6. 2. You must jump the decimal, all the way up until there is only one (1) non-zero digit out in front.
460,000,000,000,000,000,000,000.
3. Be sure to count the jumps.

7. 4. The number of jumps will be your exponent
460,000,000,000,000,000,000,000.
If you are jumping to the left , your exponent will be POSITIVE.
If you are jumping to the right , your exponent will be NEGATIVE.

8. 5. After you have moved your decimal, you may get rid of all non sig figs.
460,000,000,000,000,000,000,000
4.6
6. Multiply it by 10 (ten) and add the exponent on the 10.
4.6 X 1023
7. That’s it!

9. What if we have a number that’s less than 1.
Example:
We’re jumping to the Right, so the exponent will be negative.
Count the jumps.
Stop jumping when there is one (1) non-zero digit out in front of the decimal point.
Get rid of all non sig figs
2 X

10. Dimensional Analysis
Dimensional analysis is a method for solving problems that uses the units associated with numbers as a guide to solve the problem.
In other words, DA will let you know if you’re doing a problem right.

11. DA
DA is based on the fact that units can be multiplied and divided just like numbers can be.
What is 2/2?
What is 2 X 1?
1 2
3. What is m/m?
4. What is m X 1? m

12. DA
In DA, you convert from one unit to another. The nice thing about it is that it will let you know if you’re right by either giving you the correct units, or the wrong units.
Let’s Start simple: How many inches are in a 3.5 foot board of wood?

13. DA How many inches are in a 3.5 foot board of wood?
What are we trying to find?
-How many inches are in this board that’s a couple feet long.
2. What are we converting from (where do we start)?
We’re starting with a 3.5 foot board.
3. What unit are we converting to (where do we end)?
- We want the units to be in inches.

14. DA How many inches are in a 3.5 foot board of wood?
4. So we start with 3.5 feet.
3.5 feet
5. Then we multiply it by what is known as a CONVERSION FACTOR. A conversion factor is just a ratio that you use to cancel out units.

15. Conversion factors Examples of conversion factors are: 1 in = 2.54 cm
1 gal = 16 cups
48 tsp. = 1 cup
5.0 ml = 1 teaspoon

16. 3.5 feet to inches
Start with the number and unit to be converted. Place this number over 1.
3.5 feet 1
Then multiply by the conversion factor (1 foot = 12 inches). Whatever unit you want to cancel will be on OPPOSITE SIDES of the bar so they cancel out.
3.5 feet X 12 inches
1 1 foot

17. 3.5 feet to inches
Cancel out what units cancel and then multiply remaining numbers and units to find your answer.
= 42 inches
3.5 feet X 12 inches
1 1 foot

18. This man just received the world record for having the biggest biceps ever! He can curl grams! What is that in pounds?
(1 pound = grams)

19. 500 pounds!
Chem

20. If this Body builder lifts for six hours a day, how many minutes a week is that?