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Scientific Notation

Scientific Notation. Scientific Notation. A number is expressed in scientific notation when it is in the form a x 10 n where a is 1 or greater, but less than 10 and n is an integer. When using Scientific Notation, there are two kinds of exponents: positive and negative.

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Scientific Notation

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  1. Scientific Notation

  2. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10n where a is 1 or greater, but less than 10 and n is an integer

  3. 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

  4. When changing scientific notation to standard notation, the exponent tells you which direction to 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!

  5. When changing scientific notation to standard notation, the exponent tells you which direction to 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!

  6. 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.

  7. 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.

  8. 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.

  9. Try changing these numbers from Scientific Notation to Standard Notation: • 9.678 x 104 • 7.4521 x 10-3 • 8.513904567 x 107 • 4.09748 x 10-5 96780 .0074521 85139045.67 .0000409748

  10. When changing from Standard Notation to Scientific Notation: 1) First, move the decimal after the first counting 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

  11. 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

  12. Try changing these numbers from Standard Notation to Scientific Notation: • 9872432 • .0000345 • .08376 • 5673 9.872432 x 106 3.45 x 10-5 8.376 x 102 5.673 x 103

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