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# Scientific Notation

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### Scientific Notation

1. 1. Scientific Notation 06/01/09 PH 8.5 Bitsy Griffin
2. 2. Scientific Notation <ul><li>A number is written in scientific notation if it is in the form </li></ul><ul><li>a ● 10 x </li></ul><ul><li>Most of this lesson should be review for you </li></ul>06/01/09 PH 8.5 Bitsy Griffin
3. 3. Standard Notation <ul><li>This is how we see numbers day to day. </li></ul><ul><li>8,904,000 is in standard notation. </li></ul><ul><li>8.904 x 10 6 is in scientific notation. </li></ul>06/01/09 PH 8.5 Bitsy Griffin
4. 4. Scientific Notation <ul><li>Scientific notation is a way to reformat numbers </li></ul><ul><li>Very large or very small numbers can be cumbersome to write </li></ul><ul><li>Scientific notation makes them easier to write </li></ul>06/01/09 PH 8.5 Bitsy Griffin
5. 5. Scientific Notation <ul><li>All numbers in scientific notation should start with: </li></ul><ul><li>1 to 9 </li></ul><ul><li>If it starts with any other number, then you need to look at your answer and see what happened. </li></ul>06/01/09 PH 8.5 Bitsy Griffin
6. 6. Scientific Notation <ul><li>Numbers greater than 1 will have an exponent that is a positive number. </li></ul><ul><li>When you convert these numbers back from scientific notation to standard form, move the decimal to the right. </li></ul>06/01/09 PH 8.5 Bitsy Griffin
7. 7. Scientific Notation <ul><li>Decimals will have an exponent that is a negative number. </li></ul><ul><li>When you convert these numbers back from scientific notation to standard form, move the decimal to the left. </li></ul>06/01/09 PH 8.5 Bitsy Griffin
8. 8. Calculator Tip <ul><li>On your calculator: </li></ul><ul><li>5.34E9 = 5.34 x 10 9 </li></ul><ul><li>Also, let’s round numbers to the hundredths place for this lesson. </li></ul>06/01/09 PH 8.5 Bitsy Griffin
9. 9. Example 1 <ul><li>18,900,000,000 </li></ul><ul><li>Place the decimal at the end where it belongs and then behind the first significant digit. </li></ul><ul><li>Count the digits between the two decimals for the exponent. This is a positive exponent because since it started out as a number greater than 1. </li></ul><ul><li>1.8 900 000 000. </li></ul><ul><li>1.89 x 10 10 </li></ul>06/01/09 PH 8.5 Bitsy Griffin
10. 10. Example 1 <ul><li>0.000 000 007 65 </li></ul><ul><li>Place the decimal at the appropriate spot where it belong. </li></ul><ul><li>Count the digits between the two decimals for the exponent. This is a negative exponent because since it started out as a decimal. </li></ul><ul><li>0.000 000 00 7. 65 </li></ul><ul><li>7. 65 x 10 - 9 </li></ul>06/01/09 PH 8.5 Bitsy Griffin
11. 11. Example 1 <ul><li>4.5 million </li></ul><ul><li>Write out million. </li></ul><ul><li>1 000 000 </li></ul><ul><li>Enter it in your calculator </li></ul><ul><li>4.5 x 1000000 </li></ul><ul><li>4500000 </li></ul><ul><li>4.5 x 10 6 </li></ul>06/01/09 PH 8.5 Bitsy Griffin
12. 12. Example 2 <ul><li>2 x (3.7 x 10 -5 ) </li></ul><ul><li>Put this in your calculator </li></ul><ul><li>7.4E-5 </li></ul><ul><li>Convert to scientific notation </li></ul><ul><li>7.4 x 10 -5 </li></ul>06/01/09 PH 8.5 Bitsy Griffin
13. 13. Example 2 <ul><li>(3.5 x 10 10 ) ÷ 5 </li></ul><ul><li>Put this in your calculator </li></ul><ul><li>7 000 000 000 </li></ul><ul><li>Convert to scientific notation </li></ul><ul><li>7.0 x 10 9 </li></ul>06/01/09 PH 8.5 Bitsy Griffin
14. 14. Example 3 <ul><li>(5.72 x 10 3 ) / (6.11 x 10 -4 ) </li></ul><ul><li>Notice that these are not written with ( ) – make sure that you add them! </li></ul><ul><li>What will happen if you don’t? </li></ul><ul><li>Put this in your calculator </li></ul><ul><li>9 361 702.128 (what are we rounding to?) </li></ul><ul><li>Convert to scientific notation </li></ul><ul><li>9.36 x 10 6 </li></ul>06/01/09 PH 8.5 Bitsy Griffin
15. 15. Example 3 <ul><li>(7.9 x 10 -13 ) (6.41 x 10 10 ) </li></ul><ul><li>Put this in your calculator </li></ul><ul><li>.050 636 </li></ul><ul><li>(what are we rounding to?) </li></ul><ul><li>Convert to scientific notation </li></ul><ul><li>5.06 x 10 -2 </li></ul>06/01/09 PH 8.5 Bitsy Griffin