Significant Figures and Scientific Notation

Date: 05/21/97 at 15:31:21
From: Tom Smith
Subject: Physics

1) Round off 0.0049064 to four significant figures
  
2) How many significant figures does 1.00 have?

I have trouble with significant figues. I don't know if I should count 
the numbers after the decimal point. I have to give a presentation in 
class about sig figs and I need to know if these problems are correct. 

Thank you.

Date: 06/05/97 at 19:59:23
From: Doctor Mandel
Subject: Re: Physics

Tom,

To use significant figures, you need to first put the number into 
scientific notation.  Scientific notation means writing a number as 
the first digit before the decimal and the rest of the number after 
the decimal (up to the zeros) all multiplied by a power of ten.  

For example, to write 12300 in scientific notation, you write the 
first digit before the decimal point and the rest of the digits after 
it, so you write 1.23.  Then you figure out by what power of ten you 
have to multiply 1.23 by to get 12300. It's easier to think of this 
as, "How many decimal places do I have to move the decimal point to 
the left?"  In this case, it would be 4 places to the left, so the 
full number would be 1.23 * 10^4.  This number has three significant 
figures since, when written in scientific notation it has three 
digits.  If the number is less than zero (.003 for example), you count 
how many places you move the decimal to the left to give you a 
negative number, so the power of ten is negative.
   
Moving on to your problems, if you were to write 0.0049064 in 
scientific notation, you would write 4.9064 * 10^-3.  This number has 
five significant figures since it is 4.9064, so to make it four 
significant figures you round it off until there are four digits, so 
you would make it 4.906 * 10^-3.
   
If in a number there are zeros after the decimal point, they are there 
for a reason and should be counted as significant figures.  Using 
another of your examples, 1.00 (* 10^0) has three significant figures 
because there are three digits present, not counting the ten to the 
whatever power.  

-Doctor Mandel,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/