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Scientific Notation

Scientific Notation. When scientists deal with very large numbers, it’s hard to keep track of place values!. How far ? 92000000 miles. It is hard with very small numbers, too!. How wide is an atom?. 0.0000000001 meters wide!. Scientific notation consists of two parts:.

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Scientific Notation

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  1. Scientific Notation

  2. When scientists deal with very large numbers, it’s hard to keep track of place values! How far? 92000000 miles

  3. It is hard with very small numbers, too! How wide is an atom? 0.0000000001 meters wide!

  4. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x

  5. We use Short hand ! 10 100 = 10 x 10 1,000 = 10 x 10 x 10 10,000 = 10 x 10 x 10 x 10 100,000 = 10 x 10 x 10 x 10 x 10 1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 one googol !!!

  6. Standard Form 200 = 2 x 100 4,000 = 4 x 1000 70,000 = 7 x 10,000 500,000 = 5 x 100,000 3,000,000 = 3 x 1,000,000 Scientific Notation

  7. The point moved 6 places Add the decimal point Between 1 and 10 A short cut Move the point to get a number between 1 and 10 . 8 000 000 .

  8. The point moved 7 places Add the decimal point Between 1 and 10 A short cut Move the point to get a number between 1 and 10 92 000 000 . .

  9. Try for yourself: Turn Standard Form into Scientific Notation (1) 30 000 (2) 700 000 (3) 5 300 (4) 470 000 (5) 9 500 000

  10. The point moves 5 places Zeros after the point aren’t needed. Changing back 3.46 00000 . =346,000 Hint: Add 5 zeros, although you probably won’t need them all.

  11. The point needs to move 7 places Zeros after the point aren’t needed. Changing back 8.6 0000000 . =86,000,000 Hint: Add 7 zeros, although you probably won’t need them all.

  12. Try for Yourself: Change Scientific Notation back to Standard form (1) (2) (3) (4) (5) = 600 000 = 8 000 = 650 000 = 120 000 000 = 3 710 000

  13. The point moved 10 places. Negative sign for small numbers. Standard Form to Scientific Form for SMALL numbers Move the point to get a number between 1 and 10 . 0.000 000 000 1

  14. The point moved 7 places. Negative sign for small numbers. Standard Form to Scientific Notation for small numbers Move the point to get a number between 1 and 10 . 0.000 000 76

  15. The point moved 6 places. Negative sign for small numbers. Standard Form to Scientific Notation for small numbers Move the point to get a number between 1 and 10 0.000 001 93 .

  16. Try for Yourself: Change Standard Form to Scientific Notation (1) 0.000 07 (2) 0.000 45 (3) 0.003 4 (4) 0. 000 724 (5) 0.000 000 494

  17. -3 so remember to move point left3 spaces. Changing back small numbers Hint: Add 3 zeros to the left of the number. = 0.002 2 000 . .

  18. -5 so remember to move point left for small numbers. Changing back small numbers Hint: Add 5 zeros to the left of the number. 8.6 00000 . = 0.000 086

  19. -6 so remember to move point left for small numbers. Changing back small numbers Hint: Add 6 zeros to the left of the number. 5.16 000000 . = 0.000 00516

  20. Try for Yourself: Change Scientific Notation to Standard form (1) (2) (3) (4) (5) = 0.0005 = 0.00009 = 0.0058 = 0.000 000 62 = 0.000 000 006 032

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