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# Scientific Notation

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### Scientific Notation

1. 1. Scientific Notation
2. 2. Scientific Notation <ul><li>Allows us to write very big and very small numbers </li></ul>
3. 3. Scientific Notation <ul><li>Every number written in scientific notation has two basic parts.  </li></ul><ul><ul><li>The first part is always a decimal number between 1.00 and 9.99… </li></ul></ul><ul><ul><li>The second part is 10 times some exponent </li></ul></ul>
4. 4. Scientific Notation <ul><li>3.42 x 10 6 or 8.005 x 10 -3 </li></ul><ul><li>Notice that in each of these, the first part is a decimal number between 1.00 and 9.99… </li></ul>
5. 5. Scientific Notation <ul><li>3.42 x 10 6 means </li></ul><ul><li>3.42 x (10 x 10 x 10 x 10 x 10 x 10)   </li></ul><ul><li>or 3420000 </li></ul>
6. 6. Scientific Notation <ul><li>8.005 x 10 -3 means </li></ul><ul><li>8.005 x (0.1 x 0.1 x 0.1) </li></ul><ul><li>  or 0.008005 </li></ul>
7. 7. Scientific Notation <ul><li>the exponent on the 10 tells you which direction to move the decimal and how many times it should be moved. </li></ul><ul><ul><li>POSITIVE EXPONENT means move RIGHT </li></ul></ul><ul><ul><li>NEGATIVE EXPONENT means move LEFT </li></ul></ul>
8. 8. Scientific Notation <ul><li>Can I change standard notation to scientific notation? </li></ul><ul><ul><li>Let's say you wanted to convert the following number to scientific notation: </li></ul></ul><ul><ul><li>0.00000782 </li></ul></ul>
9. 9. Scientific Notation <ul><li>The first part has to be between 1.00 and 9.99... </li></ul><ul><li>Move your decimal until you have a number that qualifies </li></ul><ul><li>7.82 </li></ul>
10. 10. Scientific Notation <ul><li>Remember that the exponent tells you the number of spaces that you moved it.  So the answer is either </li></ul><ul><li>7.82 X 10 6 or 7.82 X 10 -6 </li></ul>
11. 11. Scientific Notation <ul><li>A standard notation number LOWER than 1 means NEGATIVE exponent </li></ul><ul><li>A standard notation number GREATER than 1 means POSITIVE exponent </li></ul>
12. 12. Scientific Notation <ul><li>1) 3,400 </li></ul><ul><li>2) 0.000023 </li></ul><ul><li>3) 101,000 </li></ul><ul><li>4) 0.010 </li></ul>
13. 13. Scientific Notation <ul><li>5) 45.01 </li></ul><ul><li>6) 1,000,000 </li></ul><ul><li>7) 0.00671 </li></ul><ul><li>8) 4.50 </li></ul>