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MAT0028 Additional resources - Oliver: Scientific Notation

A collection of videos and handouts that students may find helpful

Scientific Notation

 Ø Scientific Notation  -   To write a number in Scientific Notation

  • Step 1:  Move the decimal point in the original number so that the new number has a value between 1 and 10.
     
    3,456,789 ==>  3.456789 (The new number is now between 1 and 10), (The decimal point was moved 6 places)
      
    0.000945432 ==> 9.45432 (The new number is now between 1 and 10), (The decimal point was moved 4 places)
       
      
  • Step 2:  Count the number of decimal places the decimal point is moved (…in Step 1).  If the original number was 10 or greater, the count is positive.  If the original number was less than 1, the count is negative.
      
  • Step 3:  Multiply the new number in Step 1 by 10 raised to an exponent equal to the count found in Step 2
     
     
    (for Example)  0.000003   = 3.0 x 10−6     
                 
    367,000,000  = 3.67 x 108

 

 

 

Some other examples.

A number written in scientific notation can be written in standard form.

  • 8.63 x 103 = 8.63 x (1000) = 8630
      
    (
    Notice the exponent is positive 3 and we moved the decimal point three places to the right.)
  • 3.489 x 10−6 = 3.489 x (.0000001) = 0.000003489
      
    (
    Notice the exponent is negative 6 and we moved the decimal point six places to the left.)

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