1. REALLY, REALLY SMALL NUMBERS.
SCIENTIFIC NOTATION
A QUICK WAY TO WRITE
REALLY, REALLY BIG OR
REALLY, REALLY SMALL NUMBERS.

2. Mathematicians are Lazy!!!
They decided that by using powers of 10, they can create short versions of long numbers.

3. Rules for Scientific Notation
To be in proper scientific notation the number must be written with
* a base number > 1 and < 10
* and multiplied by a power of ten
Example X 105

4. Soooo
137,000,000 can be rewritten as
1.37 X 10⁸ or
1.4 x 10⁸

5. Using scientific notation, rewrite the following numbers.
Now You Try
Using scientific notation, rewrite the following numbers.
347,000
3.5 X 105
902,000,000
9.0 X 108
61,400
6.1 X 104

6. Convert these to standard form
1.23 X , X 106 6,806,000

7. Try These
4, X X 103 2, X 106 6,123, ,000, X 108

8. In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation. 1.5 X 107

9. The U.S. has a total of X 107 acres of land reserved for state parks. Write this in standard form.
12,916,000 acres

10. Why does a Negative Exponent give us a small number?
10000 = 10 x 10 x 10 x 10 = 104
= 10 x 10 x 10 = 103
= 10 x 10 = 102
= 101
1 = 100
Do you see a pattern?

11. Sooooo
= 10-1
= = 10-2
= = 10-3
= = 10-4

12. Using Scientific Notation, rewrite the following numbers.
Your Turn
Using Scientific Notation,
rewrite the following numbers.
8.8 X 10-4
5.9 X 10-7
4.0 X 10-5

13. More Examples 4.0 X 10-4 2) 1.248 X 10-6 .000001248 3) 6.123 X 10-51)
4.0 X 10-4
2) X 10-6
3) X 10-5 4)
3.1 X 10-6 5)
8.9 X 10-4

14. .000007 The nucleus of a human cell is about
7 X 10-6 meters in diameter. What is the length in standard notation?

15. A ribosome, another part of a cell, is about 0
A ribosome, another part of a cell, is about of a meter in diameter. Write the length in scientific notation. 3 X 10-9

16. Rules for Moving the Decimal when writing in Scientific Notation
If you move the decimal to the left, the exponent of 10 will be :
Positive
The number of places you moved the decimal.
If you move the decimal to the right, the exponent of 10 will be :
Negative

17. When writing a number from Scientific Notation to Standard Form
If the exponent is positive, move the decimal to the right the number of places the exponent is If the exponent is negative, move the decimal to the left the number of places the exponent is

18. Another way to remember Both!
If the number is BIG (larger than 1), the exponent will be POSITIVE. If the exponent is POSITIVE, the number will be BIG. If the number is SMALL (less than 1), the exponent will be NEGATIVE. If the exponent is NEGATIVE, the number will be SMALL.