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  Math B

Scientific Notation
 

As you already know, scientific notation (or exponential notation) is a concise way to express very small or very large numbers.

Consider the speed of light, 300,000,000 m/sec.  When writing this value it is very easy to "lose" one, or more, of the zeros.  It is much faster and easier to write 3.0 x 108  or  3.0E+8.

Correctly written scientific notation has two components:

(1) a number between 1 and 10
               
multiplied by....

(2) a power of 10.  

 

One of the advantages of scientific notation is its ease of use when performing computations.
 Watch the laws of exponents at work!

To multiply two numbers expressed in scientific notation, simply multiply the numbers out front and add the exponents.  Generically speaking:

(n x 10a) (m x 10b) = (n · m) x 10a+b

Example: (5.1 x 104) (2.5 x 103) = 12.75 x 107   Oops!!
This new answer is no longer in proper scientific notation.
Proper scientific notation is 1.275 x 108

To divide two numbers expressed in scientific notation, simply divide the numbers out front and subtract the exponents.  Generically speaking:

(n x 10a) / (m x 10b) = (n / m) x 10a-b

Example: (6.2 x 106) (3.1 x 103) = 2.0 x 103 

Example: (3.66 x 10-5) (2.0 x 10-3) = 1.83 x 10-2
Watch out for those negative exponents!!! 

To add (or subtract) two numbers expressed in scientific notation, be sure that the exponents in each number are the SAME.  Generically speaking:

(n x 10a) + (m x 10a) = (n + m) x 10a

or

(n x 10a) - (m x 10a) = (n - m) x 10a

If the exponents are NOT the same, the decimal of one of the numbers has to be repositioned so that it's exponent is the same as the other number being added or subtracted.  Think of it as lining up the decimals for addition or subtraction.

Example: (3.2 x 105) + (5.1 x 104) =
(3.2 x 105) + (0.51 x 105) = 3.71 x 105

 

 


           F. Roberts