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Scientific Notation. Ch. 3. Scientific Notation. We use scientific notation because we deal with very large and very small numbers. Scientific notation is written as a product of 2 numbers. The first is a coefficient, and the second is 10 raised to a power called an exponent.

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Scientific notation1
Scientific Notation

  • We use scientific notation because we deal with very large and very small numbers.

  • Scientific notation is written as a product of 2 numbers. The first is a coefficient, and the second is 10 raised to a power called an exponent.

    Coefficient is always a number greater than 1 and less than 10.

    The exponent equals the number of places the original decimal point has been moved to write in scientific notation.


Scientific notation2
Scientific Notation

  • When moving the decimal to the left, the exponent is positive

    Ex. 1 36,000 is written as 3.6 X 104

  • When moving the decimal to the right, the exponent is negative

    Ex. 20.0081 is written as 8.1 X 10-3


Multiplying using scientific notation
Multiplying using scientific notation

  • To multiply, simply multiply the coefficients and add the exponents

    Ex. (3.0 X 104) x (2.0 X 102)

    (3.0 x 2.0) X 10 4+2

    6.0 X 106


Dividing using scientific notation
Dividing using scientific notation

  • To divide, simply divide the coefficients and subtract the exponents.

  • Ex. (3.0 X 104) / (2.0 X 102)

    (3.0 / 2.0) X 10 4-2

    1.5 X 102


Addition or subtraction using scientific notation
Addition or subtraction using scientific notation

  • To add or subtract, the exponents must be made to be the same. This is like lining up the decimal when we add or subtract.

    Ex. (5.40 X 103) + (6.0 X 102)

    First, make the exponent the same

    (5.40 X 103) + (.60 X 103)

    Now just add or subtract the coefficients

    (5.4 + .60) X 103 = 6.0 X 103


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