Warm Up <ul><li>Simplify. </li></ul>
Warm Up <ul><li>Simplify. </li></ul>
Scientific Notation Making the writing of REALLY BIG NUMBERS easier And really small ones, too.
Approximate Distance to Betelgeuse <ul><li>6,000,000,000,000,000  </li></ul><ul><li>miles away </li></ul>
Approximate Distance to  Proxima Centauri   <ul><li>4.3 light years  </li></ul><ul><li>4.3 x 186, 000 m/s x 60s x 60 m x 2...
Approximate Distance to  S irius A   <ul><li>4.3 light years  </li></ul><ul><li>8.6 x 186, 000 m/s x 60s x 60 m x 24 hr x ...
Big Numbers to write with less zeros <ul><li>271,209,600,000 </li></ul><ul><li>135,604,800,000 </li></ul><ul><li>39,900,00...
271,209,600,000 <ul><li>Step one: </li></ul><ul><li>How many places can we move the decimal to just inside the left most d...
Now insert the new decimal place and eliminate the end zeros. <ul><li>2.71209600000 </li></ul><ul><li>and eliminate the en...
2.712096 x 10  ? <ul><li>We can multiply 2.712096 x 100,000,000,000 to get back to our original number. </li></ul><ul><li>...
Rules for Scientific Notation <ul><li>The first number MUST be between 1 and 10 </li></ul><ul><li>The operation is multipl...
Change us! <ul><li>135,604,800,000 </li></ul><ul><li>39,900,000,000,000 </li></ul><ul><li>271,209,600 </li></ul><ul><li>Cl...
Change us to these answers. <ul><li>135,604,800,000 =  </li></ul><ul><li>1.356048 x 10 11 </li></ul><ul><li>39,900,000,000...
Let’s review <ul><li>To change 34,000,000,000,000,000 to scientific notation. </li></ul><ul><li>Count the places from the ...
Very Small Numbers <ul><li>Let’s try 0.000079 as a number in scientific notation. </li></ul><ul><li>Recall that negative e...
How many places do we need to move the decimal.  0.000079 <ul><li>We’ll end up with 7.9  </li></ul><ul><li>(between 1 and ...
Write in scientific notation:  0.003011 <ul><li>How far to move the decimal? </li></ul><ul><li>What number will be between...
Try Some <ul><li>0.00004588 </li></ul><ul><li>0.000307 </li></ul><ul><li>0.0027 </li></ul><ul><li>Convert to scientific no...
Try Some Answers <ul><li>0.00004588 = 4.588 x 10 -5 </li></ul><ul><li>0.000307 = 3.07 x 10  -4 </li></ul><ul><li>0.0027 = ...
How do I combine numbers in scientific notation? <ul><li>(8.2 x 10 6 )(3.1 x 10 6 ) </li></ul><ul><li>8.2 x 3.1 = 25.42 </...
Try One. <ul><li>(1.9 x 10 8 )(2 x 10 10 ) </li></ul><ul><li>1.9 x 2 = 3.8 </li></ul>
Try One Answer <ul><li>(1.9 x 10 8 )(2 x 10 10 ) </li></ul><ul><li>1.9 x 2 = 3.8 </li></ul><ul><li>Answer  3.8 x 10  18 </...
Try a Division Statement
Division Statement Answer
Assignment <ul><li>Page 403: 15 – 55 odds </li></ul>
 
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8 5 Scientific Notation

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8 5 Scientific Notation

  1. 1. Warm Up <ul><li>Simplify. </li></ul>
  2. 2. Warm Up <ul><li>Simplify. </li></ul>
  3. 3. Scientific Notation Making the writing of REALLY BIG NUMBERS easier And really small ones, too.
  4. 4. Approximate Distance to Betelgeuse <ul><li>6,000,000,000,000,000 </li></ul><ul><li>miles away </li></ul>
  5. 5. Approximate Distance to Proxima Centauri <ul><li>4.3 light years </li></ul><ul><li>4.3 x 186, 000 m/s x 60s x 60 m x 24 hr x 365 days is approximately </li></ul><ul><li>135,604,800,000 miles </li></ul><ul><li>Or </li></ul><ul><li>39,900,000,000,000 km </li></ul>Graphic from http://heasarc.gsfc.nasa.gov/ docs/cosmic/nearest_star_info.html
  6. 6. Approximate Distance to S irius A <ul><li>4.3 light years </li></ul><ul><li>8.6 x 186, 000 m/s x 60s x 60 m x 24 hr x 365 days is approximately… </li></ul><ul><li>271,209,600,000 miles </li></ul>Image from space.com Sirius is called the Dog Star
  7. 7. Big Numbers to write with less zeros <ul><li>271,209,600,000 </li></ul><ul><li>135,604,800,000 </li></ul><ul><li>39,900,000,000,000 </li></ul><ul><li>What should we use? </li></ul><ul><li>How about Scientific Notation? </li></ul>
  8. 8. 271,209,600,000 <ul><li>Step one: </li></ul><ul><li>How many places can we move the decimal to just inside the left most digit? </li></ul><ul><li>271,209,600,000 </li></ul><ul><li>Looks like eleven places. </li></ul>
  9. 9. Now insert the new decimal place and eliminate the end zeros. <ul><li>2.71209600000 </li></ul><ul><li>and eliminate the end zeros. </li></ul><ul><li>2.712096 </li></ul><ul><li>To make 2.712096 equal to 271,209,600,000 we use a power of 10. </li></ul><ul><li>In this case, 10 11 </li></ul>
  10. 10. 2.712096 x 10 ? <ul><li>We can multiply 2.712096 x 100,000,000,000 to get back to our original number. </li></ul><ul><li>100,000,000,000 is 10 11 </li></ul><ul><li>2.712096x10 11 is written in scientific notation. </li></ul>
  11. 11. Rules for Scientific Notation <ul><li>The first number MUST be between 1 and 10 </li></ul><ul><li>The operation is multiplication </li></ul><ul><li>The second number is a power of 10. </li></ul><ul><li>Check this with the above rules: </li></ul><ul><li>.9808 x 10 5 </li></ul><ul><li>Better: 9.808 x 10 4 </li></ul>
  12. 12. Change us! <ul><li>135,604,800,000 </li></ul><ul><li>39,900,000,000,000 </li></ul><ul><li>271,209,600 </li></ul><ul><li>Click for the next slide’s answers </li></ul>
  13. 13. Change us to these answers. <ul><li>135,604,800,000 = </li></ul><ul><li>1.356048 x 10 11 </li></ul><ul><li>39,900,000,000,000 = </li></ul><ul><li>3.99 x 10 13 </li></ul><ul><li>271,209,600 = </li></ul><ul><li>2.712096 x 10 8 </li></ul>
  14. 14. Let’s review <ul><li>To change 34,000,000,000,000,000 to scientific notation. </li></ul><ul><li>Count the places from the far right to the place just to the right of the left-most digit (3). That’s 16 places. </li></ul><ul><li>That’s the power of ten. In this case, 10 16 </li></ul><ul><li>Get rid of the extra unneeded zeros and multiply by the chosen power of ten. </li></ul><ul><li>3.4 x 10 16 </li></ul>
  15. 15. Very Small Numbers <ul><li>Let’s try 0.000079 as a number in scientific notation. </li></ul><ul><li>Recall that negative exponents show fractions. </li></ul><ul><li>The above number as a fraction would be seventy-nine millionths. </li></ul>
  16. 16. How many places do we need to move the decimal. 0.000079 <ul><li>We’ll end up with 7.9 </li></ul><ul><li>(between 1 and 10). </li></ul><ul><li>7.9 x 10 -? </li></ul><ul><li>7.9 x 10 -5 </li></ul>
  17. 17. Write in scientific notation: 0.003011 <ul><li>How far to move the decimal? </li></ul><ul><li>What number will be between 1 and 10? </li></ul><ul><li>Since the number is less than one, we’ll have a negative decimal. </li></ul><ul><li>3.011 x 10 -3 </li></ul>It's OK to have negative exponents in sci-notation!
  18. 18. Try Some <ul><li>0.00004588 </li></ul><ul><li>0.000307 </li></ul><ul><li>0.0027 </li></ul><ul><li>Convert to scientific notation. </li></ul>
  19. 19. Try Some Answers <ul><li>0.00004588 = 4.588 x 10 -5 </li></ul><ul><li>0.000307 = 3.07 x 10 -4 </li></ul><ul><li>0.0027 = 2.7 x 10 -3 </li></ul>
  20. 20. How do I combine numbers in scientific notation? <ul><li>(8.2 x 10 6 )(3.1 x 10 6 ) </li></ul><ul><li>8.2 x 3.1 = 25.42 </li></ul><ul><li>10 6 x 10 6 = 10 12 </li></ul><ul><li>25.42 x 10 12 needs adjustment. </li></ul><ul><ul><li>(The 25.42 is NOT between 1 and 10) </li></ul></ul><ul><li>2.542 x 10 13 </li></ul>
  21. 21. Try One. <ul><li>(1.9 x 10 8 )(2 x 10 10 ) </li></ul><ul><li>1.9 x 2 = 3.8 </li></ul>
  22. 22. Try One Answer <ul><li>(1.9 x 10 8 )(2 x 10 10 ) </li></ul><ul><li>1.9 x 2 = 3.8 </li></ul><ul><li>Answer 3.8 x 10 18 </li></ul>
  23. 23. Try a Division Statement
  24. 24. Division Statement Answer
  25. 25. Assignment <ul><li>Page 403: 15 – 55 odds </li></ul>

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