Scientific Notation

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Scientific Notation
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What is Scientific Notation?

• Scientific notation is a way of writing numbers
• It is very convenient to express numbers that are
  too large or too small to be written in decimal
  form in a simpler way
• Try multiplying 1,234,000,000,000 by 0.000005789
  is there an easy way to write the result?
• Scientific notation allows us to write and handle
  numbers in a concise manner
• Why would it be beneficial to write numbers in
  scientific notation?
• When do you use very large or very small numbers
  anyway?

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Two Parts to Scientific Notation

• Numbers written in scientific notation look like
  to following
• N x 10X
• Read it as N times TEN to the power of X
• Notice that there are two main components
• N, which is called the Mantissa
• N can be any number
• X, which is called the Exponent
• X MUST be an integer

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Pop Quiz
N x 10X

• Are the following numbers written in scientific
  notation?

4.8756 x 1000
.01867x109
2.37895 x 102
22.479x10-4
239 x 1004
9.74 x 104,660
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Converting Standard Form to Scientific Notation
N x 10X

• Put the decimal point after the first, second, or
  third digit.
• The leftmost digit should always be between 1-9
  it CANNOT be a ZERO
• Count the number of places that the decimal point
  was moved from its original location. This
  number will be your exponent
• If the new position of the decimal point is to
  the left of its original, the exponent is treated
  as positive
• If the new position of the decimal point is to
  the right of its original, the exponent is
  negative

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Examples
N x 10X

• Converting standard form to scientific notation

248 2.48x102 0.0000547 5.47x10-5 0.0348987
3.48987x10-2 4,378,000,000
4.378x109 314,150,000,000,000 31.415x1013
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Converting Scientific Notation to Standard Form
N x 10X

• Notice two things
• The location of the decimal point in the mantissa
• The sign of the exponent
• If the sign of the exponent is positive, move the
  decimal point in the mantissa X digits to the
  right
• If the sign of the exponent is negative, move the
  decimal point in the mantissa X digits to the
  left
• Fill in any empty spaces between the last number
  in the mantissa and the new position of the
  decimal point with ZEROS

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Examples
N x 10X

• Converting scientific notation to standard form

3.086x106 3,086,000 547x10-4
.0547 5.8756x102 587.56 43.995005x1010
439,950,050,000 .5x101 5