Expert: Steve Holleran - 2/6/2008

Question
Express each of the following using scientific notation

a. 45000

b. 0.000067

Answer
Hi Robert,

Okay, in scientific notation, you want to write your number as the product of a number between 1 and 10 times a power of 10.

So, for 45,000:

Suppose I asked you to put a decimal point in this number so that it became a number between 1 and 10.  Wouldn't you place it between the 4 and 5?:

       45000 = 4.5000  

Now, count from where you put the decimal to where it began(at the right end of the whole number): 4 places.  This will be the power of 10:

       45000 = 4.5 * 10^4

Similarly, 6000 = 6 * 10^3

          246,000 = 2.46 * 10^5  (Notice that you drop off the end zeros when you do this.

For 0.000067, you do the same thing, but use a negative power to indicate that the decimal would go left to get the original number back:

   0.000067-----> 6.7 * 10^-5

Hope you can understand this okay.

Steve