1. Scientific Notation
Why Do We Need It?

2. The “Size” of the Numbers
Chemistry deals with very large and very small numbers
6.02 x (Avogadro’s #) (lots of atoms)
1.5 x (size of an atom)

3. Big and Small Numbers
How do we keep track of all those zeroes?
x /
Worse yet… calculations with those numbers
Better in Scientific Notation
(6.63 x 10 –31 x 3.0 x 10 10) /9.116 x 10-8
Now… more compact, better represents significant figures and is easier to calculate

4. This lesson will show you:
1. How to write numbers in scientific notation
2. How to convert to and from scientific notation
3. How to correctly do scientific notation on your calculator
4. How to calculate numbers in scientific notation

5. Format for Scientific Notation
X = 1< N > 10 x 10 some positive or negative integer
The decimal point is in correct location if it is behind the first non-zero digit.
If 0< x> 1 the X = N x 10 negative number
If 1< X < 10 then X = N x 100
If X > 10 then X = N x 10Positive number

6. Examples
8.7 x 10-4
9.8 x 100
9.8
2.3 x 107

7. First Explanation Start at the decimal point of the original number
Count the number of decimal places you move to get to one place to the left of the decimal
The number of places you move is the exponent. Left it’s a positive value…..right is a negative value

8. Second Explanation
Write all digits down with the decimal point just to the right of the first significant digit. This should always result in a value between 1 and 10
Now count how many decimal places you would move to recover the original number.
If you count to the left the exponent is negative. To the right is positive.

9. Correcting Incorrect Scientific Notation
428.5 x 109
Write the integer as a number between 1 and 10
Correct the exponent

10. From Scientific to Decimal
Exponential notation
Normal Notation
1.25 x 102
6.83 x 10-2
3.35 x 10-8
9.33 x 1012
125
.0 683

11. Math with Scientific Notation Addition and Subtraction
All exponents MUST BE THE SAME before you can add and subtract numbers in scientific notation. The actual addition or subtraction will take place with the numerical portion, NOT the exponent.
A good rule to follow is to express all numbers in the problem in the highest power of ten

12. Math with Scientific Notation Multiplication and Division
Multiplication: Multiply the decimal portions and add the exponential portions.
Division: Divide the decimal portions and subtract the exponential portions.

13. Examples
1.39 X 10-3
(3.05 x 106) x (4.55 x 10¯10) =
(3.05 x 106) + (4.55 x 104) =
3.10 x 106
3.68 x 104
(1.05 x 108) / (2.85 x 103) =
(9.33 x 10-13) - (4.55 x 10-14) =
8.88 x 10-13

14. Using Your Calculator
Speaking realistically, the problems discussed can all be done on a calculator.
However, you need to know how to enter values into the calculator, read your calculator screen, and round off to the proper number of significant figures.
Your calculator will not do these things for you.

15. The EXP Key
The right way involves the use of a key usually marked "EXP" or "EE." A usual wrong way involves using the times key, where the student presses times then 10 then presses the "EXP" key.

16. What to know about your calculator
Be sure you know how to put your calculator into scientific notation.
Be sure you know how to take it out of scientific notation.
Know how you calculator reports exponents.