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Converting To and From Scientific Notation

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Converting To and From Scientific Notation

Converting To Scientific Notation

To Change from Standard Form to Scientific Notation:

  1. Place the decimal point such that there is one non-zero digit to the left of the decimal point.
  2. Count the number of decimal places the decimal has “moved” from the original number. This will be the exponent of the 10.
  3. If the original number was less than 1, the exponent is negative; if the original number was greater than 1, the exponent is positive.

Converting To and From Scientific Notation 1
Examples:

  1. Given: 4,750,000
    4.75 (moved decimal point 6 decimal places)
    Answer: 4.75 × 106
    The original number was greater than 1 so the exponent is positive.
  2. Given: 0.000789
    7.89 (moved decimal point 4 decimal places)
    Answer: 7.89 × 10-4
    The original number was less than 1 so the exponent is negative.

Converting From Scientific Notation

To Change from Scientific Notation to Standard Form:

  1. Move the decimal point to the right for positive exponents of 10. The exponent tells you how many places to move.
  2. Move the decimal point to the left for negative exponents of 10. Again, the exponent tells you how many places to move.

Converting To and From Scientific Notation 2
Examples:

  1. Given: 1.015 × 10-8
    Answer: 0.00000001015 (moved decimal 8 places left)
    Negative exponent moves decimal to the left.
  2. Given: 5.024 × 103
    Answer: 5,024 (move decimal 3 places right)
    Positive exponent moves decimal to the right.

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