1. 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 number between 1 and 10
* and multiplied by a power of
ten
23 X 105 is not in proper scientific notation. Why?

4. How wide is our universe?
210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

5. 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

6. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles 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? Between the 2 and the 1

7. 2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

8. 1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative x 10-8

9. Soooo
137,000,000 can be rewritten as
1.37 X 108

10. Using scientific notation, rewrite the following numbers.
Now You Try
Using scientific notation, rewrite the following numbers.
347,000.
3.47 X 105
902,000,000.
9.02 X 108
61,400.
6.14 X 104

11. Convert these:
1.23 X , X 106 6,806,000

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

13. 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

14. 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

15. 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?

16. Using Scientific Notation, rewrite the following numbers.
Your Turn
Using Scientific Notation,
rewrite the following numbers.
8.82 X 10-4
5.9 X 10-7
4 X 10-5

17. More Examples 4 X 10-4 2) 1.248 X 10-6 .000001248 3) 6.123 X 10-51)
4 X 10-4
2) X 10-6
3) X 10-5 4)
3.06 X 10-6 5)
8.92 X 10-4

18. .000007 The nucleus of a human cell is about
7 X 10-6 meters in diameter. What is the length in standard notation?

19. 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

20. EXIT TICKET 1. 2.