Algebra: Scientific Notation

In courses such as chemistry (see our credits page for more on chemistry) or when computing Bill Gates' net worth, it is sometimes necessary to use huge numbers such as 26,890,000,000,000,000,000 (which happens to be the number of molecules of a gas in a cubic meter). Using these large (or sometimes, extremely small) numbers can easily lead to mistakes and use tons of paper! :-) Scientific notation takes care of this.

Numbers in scientific notation look like the following examples: 4.16 x 10^(+b) and 4.16 x 10^(-b). b is always a positive, real number. The 10^(+b) tells us that the decimal point is b places to the right of where it is shown. The 10^(-b) tells us that the decimal point is b places to the left of where it is shown.

Examples:

1. Write .000316 in sceintific notation.
   Solution: Start off by moving the decimal point behind the first
             digit that is not a 0 and by adding the x 10.

             3.16 x 10

             Now all you need is a value for b.  You get that by
             figuring how many places away and in which direction the
             decimal point was from where you've got it now.  It used to be
             4 places to the left, so the proper value for b is 
             -4.  The answer is 3.16 x 10^(-4).

2. Write in scientific notation: .000316 x 10^(-7)
   Solution: Write the first term, .00316 in scientific notation.

             3.16 x 10^(-4) x 10^(-7)

             Combine the last two terms (the x 10^bs) using the
             Product Theorem for Exponents.  Once
             that is done, you have the answer!

             3.16 x 10^(-11)

Take the quiz on scientific notation. The quiz is very useful for either review or to see if you've really got the topic down.

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