Scientific notation
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Scientific Notation. Basics. All numbers written in scientific notation will look like this: n x 10 a n = a number that is greater than or equal to one and less than 10 1 ≤ n < 10

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Scientific Notation

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Scientific notation

Scientific Notation


Basics

Basics

  • All numbers written in scientific notation will look like this:

    n x 10a

    n = a number that is greater than or equal to one and less than 10 1 ≤ n < 10

    a = the number of times the decimal moved when the number was in standard form.The number in standard form determines whether the exponent is positive or negative.


Positive exponent

Positive Exponent

  • The exponent will be positive if the number in standard form is greater than 1.

  • Example: 549.3This is a number greater than 1. To write this in scientific notation, move the decimal point two (2) times to the left to make a number less than 10 but greater than or equal to 1.

    5.493 5.493 X 102

    Now the power of 10 that goes with this number will have a positive exponent of 2 because we moved the decimal two times and the number was greater than 1 in standard form.


Negative exponent

Negative Exponent

  • The exponent will be negative if the number in standard form is less than 1.

  • Example: .000298 This is a number that is less than 1. To write this in scientific notation move the decimal four (4) times to the right in order to get a number less than 10 and greater than or equal to 1.

    2.982.98 x 10-4

    The power of 10 that goes with this number will have a negative exponent because the number in standard form was less than 1.


Practice problems

Practice Problems

  • Write the following numbers in scientific notation.

  • 12.92.9993..000007

  • .0565.186..000288

  • Write the following numbers back in standard form.

  • 4.3 x 10-32.9.825 x 1023.5.04 x 10-1

    4.1.0001 x 1055.3.77 x 10-46.8.1 x 103


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