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Scientific Notation Notes

Scientific Notation Notes. Challenge : Write 37.4 in scientific notation. 3.74 x 10 1. Scientific Notation is a way to write numbers following the form N x 10 E N is a number between 1 and 9 . E is an exponent , and is either positive or negative. 0.065

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Scientific Notation Notes

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  1. Scientific Notation Notes

  2. Challenge: Write 37.4 in scientific notation. 3.74 x 101

  3. Scientific Notation is a way to write numbers following the form N x 10E • N is a number between 1 and 9. • E is an exponent, and is either positive or negative.

  4. 0.065 is an example of a number in Standard Notation 6.5 x 10-2 Is an example of the same number in Scientific Notation

  5. 23.57 STANDARD 4.2 x 10 -2SCIENTIFIC 5623.08 STANDARD 0.5287 SCIENTIFIC 2.54 x 103SCIENTIFIC 7.06 x 10-8SCIENTIFIC 0.00265 STANDARD 8.5 x 107SCIENTIFIC

  6. As scientists, we see very large numbers. For example: The number of bacteria on a surface, Avogadro’s number • We also see very small numbers. For example: The size of an atom • Which notation do you think is easier to write very large and very small numbers in?

  7. Changing Standard Notation to Scientific Notation • How can we change numbers written in standard notation to scientific notation? PEL NER Positive Exponent Left Negative Exponent Right

  8. Let’s change 0.00085 from standard notation to scientific notation.Is 0.00085 greater than or less than 1?Less than 1So we know that the exponent in scientific notation is going to be Negative

  9. Reading from left to right, find the first non zero number in 0.00085 and underline it. 0.00085

  10. We want to move the decimal point behind the number you underlined. 0.00085 • Count how many loops you make to move the decimal point. • Number of loops = 4 and this number is the exponent • N = 8.5 now

  11. Go back to the top. Our exponent in scientific notation must be negative. • Therefore, our exponent in scientific notation is -4.

  12. What is the final answer in scientific notation? 8.5 x 10-4

  13. Changing Scientific Notation to Standard Notation PEL NER will NOT help out this time!

  14. Let’s change 6.35 x 10-2 into standard notation. • Is the exponent negative or positive? negative • If the exponent is negative then you will move the decimal to the left to make the number smaller. • If the exponent is positive then you will move the decimal to the right to make the number larger.

  15. Which way should we move the decimal? 6.35 x 10-2 Negative exponent- move decimal to the left

  16. The exponent tells you how many spots to move the decimal. How many? 2 places to the left • Move it! Fill loops in with zeros 06.35 x 10-2 • Your final answer in standard notation is 0.0635

  17. Multiplying and Dividing in Scientific Notation • Multiplying: • Multiply the numbers in the N spot • Add the exponents.

  18. (8.95 x 109)(4.31 x 10 -2) 8.95 x 4.31 = 38.57 9 + (-2) = 7

  19. Write the final answer in scientific notation. 38.57 x 107 BUT we want the decimal behind the FIRST non zero number! 3.857 x 108

  20. Dividing: • Divide the numbers in the N spot. • Subtract the exponents.

  21. 6.82 x 10-7 4.25 x 104 6.82 / 4.25 = 1.60 (-7) – (4) = -11

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