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# Sig fig and sci note

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### Sig fig and sci note

1. 1. Scientific Notation
2. 2. Scientific Notation <ul><li>A number written as a product of two numbers: a coefficient and a power of 10 </li></ul><ul><li>Designed for the expression of very big and very small numbers </li></ul><ul><ul><li>3.6 x 10 4 </li></ul></ul><ul><ul><li>1 gram of hydrogen contains 301,000,000,000,000,000,000,000 molecules </li></ul></ul><ul><ul><li>3.01 x 10 23 molecules </li></ul></ul><ul><li>0.00081 = 8.1 x 10 -4 </li></ul><ul><ul><li>Decimal moves 4 place to the right </li></ul></ul><ul><li>34,000 = 3.4 x 10 4 </li></ul><ul><ul><li>Decimal move 4 places to the left </li></ul></ul>
3. 3. Scientific Notation <ul><li>To make these numbers easier to work with, we put them into scientific notation. </li></ul><ul><li>Rewrite the significant digits as a number greater than one, but less than 10. </li></ul><ul><li>Count the number of places you had to move the decimal to complete step 1. </li></ul><ul><li>Write the number of decimal places moved as an exponent. </li></ul><ul><ul><li>Positive exponent greater than 1. </li></ul></ul><ul><ul><li>Negative exponent less than 1. </li></ul></ul>
4. 4. Sample Problems <ul><li>602 200 000 000 000 000 000 000 </li></ul><ul><li>Rewrite as a number greater than one but less than 10. </li></ul><ul><li>6.022 </li></ul><ul><li>Count the number of places the decimal moved. (left) </li></ul><ul><li>23 places </li></ul><ul><li>Write that number as an exponent. </li></ul><ul><li>6.022 x 10 23 </li></ul>
5. 5. How about another one? <ul><li>0.000000000000000000000000000000911 </li></ul><ul><li>Rewrite as a number greater than one but less than 10. </li></ul><ul><li>9.11 </li></ul><ul><li>Count the number of places the decimal moved. (right) 31 </li></ul><ul><li>Write that number as an exponent. </li></ul><ul><li>9.11 x 10 -31 </li></ul>
6. 6. How about the other direction? <ul><li>Speed of light in a vacuum is </li></ul><ul><li>3.00 x 10 8 m/s </li></ul><ul><li>Move the decimal 8 places to the right. </li></ul><ul><li>300 000 000 m/s </li></ul>
7. 7. One last sample <ul><li>Atomic Mass Unit </li></ul><ul><li>1.66054 x 10 -27 kg </li></ul><ul><li>Move the decimal 27 places to the left. </li></ul><ul><li>0.00000000000000000000000000166054 kg </li></ul>
8. 8. Significant Figures a.k.a.- sig figs
9. 9. Significant Digits <ul><li>The certain digits and one estimated digit of each measurement are significant. </li></ul><ul><li>Remember! Every time you make a measurement, you record all of the certain digits and one estimated digit. </li></ul>200.5 4 g
10. 10. Rules for Sig Figs <ul><li>Non zeros are always significant. </li></ul><ul><li>Zeros between non zeros are significant. </li></ul><ul><li>Zeros at the end of significant digits following a decimal point are significant. </li></ul><ul><li>*They show precision in measurement. </li></ul><ul><li>4) Place keeper zeros are NOT significant. </li></ul><ul><ul><li>Zeros preceding significant digits. </li></ul></ul><ul><ul><li>Zeros following significant digits without a decimal point. </li></ul></ul>
11. 11. Try These Examples <ul><li>7.05940 </li></ul><ul><li>Final zero significant (follows decimal point) </li></ul><ul><li>6 significant digits </li></ul><ul><li>0.00135 </li></ul><ul><li>Leading zeros Not significant (place keepers) </li></ul><ul><li>3 significant digits </li></ul><ul><li>20,400 </li></ul><ul><li>Final zeros Not significant </li></ul><ul><li>(place keepers – no decimal) </li></ul><ul><li>3 significant digits </li></ul>
12. 12. Sig Figs and Calculations <ul><li>Adding and Subtracting </li></ul><ul><li>Round to the fewest number of decimal places given in problem. (Can only have ONE estimated digit in final answer) </li></ul><ul><li>Multiplying and Dividing </li></ul><ul><li>Round to the fewest number of significant digits given in the problem. </li></ul>
13. 13. Sample Problems <ul><li>17.20 (.01) </li></ul><ul><li> 4.137 (.001) </li></ul><ul><li>+ 26.6 (.1) </li></ul><ul><li>47.937 </li></ul><ul><li>Least significant number is reported to the tenths, so round final answer to the tenths. </li></ul><ul><li>47.9 </li></ul><ul><li>14.3 (3 sig figs) </li></ul><ul><li>1.0200 (5 sig figs) </li></ul><ul><li>x 0.005 (1 sig fig) </li></ul><ul><li>0.07293 </li></ul><ul><li>Fewest number of sig figs is one, so round the final answer to one sig fig. </li></ul><ul><li>0.07 </li></ul>
14. 14. Methylene Blue