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Scientific Notation

Scientific Notation. Darrell Hobson August 25, 2010. Why Use Scientific Notation?. An Easy Way to Express: Very Large Numbers Ex. 602000000000000000000000 Very Small Numbers Ex. 0.000000000005. Writing Numbers in Scientific Notation Form. Example Problem:

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Scientific Notation

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  1. Scientific Notation Darrell Hobson August 25, 2010

  2. Why Use Scientific Notation? • An Easy Way to Express: • Very Large Numbers • Ex. 602000000000000000000000 • Very Small Numbers • Ex. 0.000000000005

  3. Writing Numbers in Scientific Notation Form Example Problem: Rewrite 45000000 in scientific notation form.

  4. 1st Step Determine which numbers to carry through into scientific notation form (Rewrite 45000000 in scientific notation form.) 1st All significant digits are carried through into scientific notation form 45000000 → 45

  5. 2nd Step Put a new decimal after the first digit (if there are more then two digits) that is carried through into scientific notation form (Rewrite 45000000 in scientific notation form.) 2nd Step 45 → 4.5

  6. 3rd Step Determine which direction you would have to move the decimal from the new location back to its original location and count the number of moves. (Rewrite 45000000 in scientific notation form.) 3rd Step 4.5 to 45000000. ^ ^ ^ ^ ^ ^ ^ 7 times right

  7. 4th Step Adding the direction and number of decimal moves to your number in scientific notation form. Right move is positive (+) and left move is negative (-). Add (x 10) to express your number. (Rewrite 45000000 in scientific notation form.) 4th Step 4.5 x 107 Answer

  8. Examples 34000000000 → 3.4 x 1010 0.0000023 → 2.3 x 10-6

  9. Taking Numbers Out of Scientific Notation Form Example Problem: Rewrite 6.4 x 10-7 as a regular decimal number.

  10. 1st Step Write down only the numbers that appear before the (x 10) without the decimal. (Rewrite 6.4 x 10-7 as a regular decimal number.) 1st 6.4 x 10-7 → 6.4

  11. 2nd Step Determine if the decimal should be moved left or right and how many times. (Rewrite 6.4 x 10-7 as a regular decimal number.) 2nd 6.4 x 10-7 = 7 times to the left

  12. 3rd Step Physically move the decimal the direction and number of times determined. (Rewrite 6.4 x 10-7 as a regular decimal number.) 3rd 6.4 → 0. ←←←←←←←64

  13. 4th Step Add zeros between new decimal location and numbers (Rewrite 6.4 x 10-7 as a regular decimal number.) 4th 0. ←←←←←←←64 → 0.00000064 Answer

  14. Examples 5.1 x 104→ 51000 -2.4 x 10-5 → -0.000024

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