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SCIENTIFIC NOTATION
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PHYSICAL SCIENCE 1
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  • Scientific notation is a convenient way of showing very large or small numbers in scientific work.  Numbers displayed in scientific notation contain a coefficient mutliplied by 10 raised to a power of an integer.  For example:

    7.82 x 108        or      1.3 x 10–6

  • This worksheet provides instructions and practice problems for common operations involving scientific notation, including use of calculators for solving problems.
Converting Decimal to Scientific Notation

  • When converting decimal to scientific notation, move the decimal in front of the first non-zero digit.  The exponent of 10 represents the number of spaces the decimal has to be moved in order to be placed in front of the  first non-zero digit.  A positive exponent results from moving the decimal to the left, while a negative exponent results from moving the decimal to the right.  For example:

                         782000000       becomes        7.82 x 108

      and

                         0.0000013        becomes        1.3 x 10–6

Note: 
In scietific notation, the coefficient indicates the number of significant figures. 
For example, the first quantity above has 3 significant figures, while the second quantity has 2 significant figures.
Calculations with Scientific Notation

  • When multiplying or dividing numbers in scientific notation, follow the following steps:
    1. Multiply or divide the coefficients.
                  
    2. Add exponents for multiplication and subtract exponents for division.
                  
    3. Reconstruct the answer so that coefficient is not less than 1 or equal or greater than 10.
Using Calculators in Scientific Notation

  • Scientific calculators can be used to perform problems with scientific notation conveniently.  The directions below apply to most common calculators.  If you need more informatin, read the operation manual for your particular calculator. 
    1. Punch the coefficient (the digit number) into your calculator.      
    2. Push the EE or EXP button.  Do NOT use the x (times) button.          
    3. Enter the exponent number.  Use the +/- button to change signs.
    4. Perform all other operations as you normally do on your calculator.

To check yourself, multiply  8.0 x 1012 times 3.5 x 108 on your calculator. 
Your answer should be 2.8 x 1021 .

Notes:

  • Be sure to enter number correctly on your calculator.  Input errors are common causes of errors in calculations.
  • Depending on your calculator, the answers at times might not appear in scientific notation.
Practice Worksheets
  • Practice worksheets and answer keys are available below.