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Scientific Notation

Learn how to recognize and utilize scientific notation, including positive and negative exponents. Understand how to convert between scientific and standard notation with ease, remembering the rules and decimal movements. Practice with examples provided.

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Scientific Notation

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  1. Scientific Notation 0806.2.1    Recognize and use scientific notation.

  2. When using Scientific Notation, there are two kinds of exponents: positive and negative Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10-7

  3. When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a positive exponent, move the decimal to the right: 4.08 x 103 = 4 0 8 Don’t forget to fill in your zeroes!

  4. When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a negative exponent, move the decimal to the left: 4.08 x 10-3 = 4 0 8 Don’t forget to fill in your zeroes!

  5. An easy way to remember this is: • If an exponent is positive, the number gets larger, so move the decimal to the right. • If an exponent is negative, the number gets smaller, so move the decimal to the left.

  6. The exponent also tells how many spaces to move the decimal: 4.08 x 103 = 4 0 8 In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

  7. The exponent also tells how many spaces to move the decimal: 4.08 x 10-3 = 4 0 8 In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

  8. Try changing these numbers from Scientific Notation to Standard Notation: • 9.678 x 104 • 7.4521 x 10-3 • 8.513 x 107 • 4.09748 x 10-5 96780 .0074521 85,130,000 .0000409748

  9. When changing from Standard Notation to Scientific Notation: 1) First, move the decimal after the first whole number: 3 2 5 8 2) Second, add your multiplication sign and your base (10). 3 . 2 5 8 x 10 3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10 3 3 2 1

  10. When changing from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one. • If the number is greater than one, the exponent will bepositive. 348943 = 3.489 x 105 • If the number is less than one, the exponent will be negative. .0000000672 = 6.72 x 10-8

  11. Try changing these numbers from Standard Notation to Scientific Notation: • 9,870,000 • .0000345 • .08376 • 5673 9.87 x 106 3.45 x 10-5 8.376 x 10-2 5.673 x 103

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