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0.1 SCIENTIFIC NOTATION

Introductory Unit

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BY THE END OF THIS LESSON I WILL…

Be able to understand what scientific notation and standard form is.

Be able to convert between scientific notation and standard form.

Be able to perform operations with scientific notation.

Be able to use these skills as basic math skills to complete the problems required from me in Physical Science 20.

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SCIENTIFIC NOTATION – JUSTIFICATION

  • Scientists often work with very large and very small numbers, however these can be cumbersome to work with. To simplify matters we write these numbers using exponents or scientific notation.

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SCIENTIFIC NOTATION – BROKEN DOWN

  • The number 123 000 000 000 in scientific notation is written as: 1.23 x 1011
    • Coefficient: this is the first number, 1.23; it must be greater than or equal to 1 and less than 10
    • Base: this is the second number, 10; in scientific notation it must always be 10

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SCIENTIFIC NOTATION – BROKEN DOWN

  • The number 123 000 000 000 in scientific notation is written as: 1.23 x 1011
    • Exponent: this is the third number, 11; this must always be an integer.
      • It can be positive when expressing a large number
        • i.e.: 123 000 000 000 = 1.23 x 1011
      • It can be negative when expressing a small number
        • i.e.: 0.0000603 = 6.03 x 10-5

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SCIENTIFIC NOTATION – LARGE & SMALL

  • 1. Large numbers - 36000 written in scientific notation is 3.6 x 104. Count the number of decimal places you move to the left and this becomes the exponent.
  • 2. Small numbers - 0.00015 written in scientific notation is 1.5 x 10-4 . Notice that a negative exponent is used when moving the decimal to the right.
  • Rule of Thumb �When you make the number smaller, make the exponent larger and when you make the number larger, make the exponent smaller.

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ADDING & SUBTRACTING WITH SCIENTIFIC NOTATION�

  • Scenario 1: Like Exponents
    • Add or subtract the numerical coefficient and keep the exponent the same. If the numerical coefficient becomes higher than 10 or lower than 1, adjust the exponent.
    • Example:
      • 4 x 104 m + 2 x 104 m = 6 x 104 m

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ADDING & SUBTRACTING WITH SCIENTIFIC NOTATION�

  • Scenario 2: Unlike Exponents
    • Change one of the exponents (usually make the smaller one larger) so both exponents are the same, then add or subtract the numerical values.
    • Example:
      • 4.0 x 10-6 m - 3 x 10-7 m
      • = 4.0 x 10-6 m - 0.3 x 10-6 m
      • = 3.7x 10-6 m

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MULTIPLYING & DIVIDING WITH SCIENTIFIC NOTATION�

  • Quantities do not need the exponents to be the same when multiplying or dividing.
  • Multiplying: Multiply the numerical coefficients and add the exponents. Don't forget to multiply the units.
    • Example:
      • (3 x 102 m) (2 x 103 m) = 6 x 105 m2

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MULTIPLYING & DIVIDING WITH SCIENTIFIC NOTATION�

  • Dividing: Divide the numerical coefficients and subtract the exponents. Remember to divide the units.
    • Example:
      • 8 x 106 m ÷ 2 x 103 s = 4 x 103 m/s