When dealing with numbers or especially when making measurements, as you will sometimes being doing in laboratory assignments for this class, it is important to be cognizant of the issue of significant digits.  These are an indication of how good measurements are.  Measurements in science are typically reported only to the extent given by the precision or accuracy of the measurements.  In the labs, I often ask you to report measurements to a certain number of digits.  Besides telling you how many digits to report, it provides an indication of how accurate I expect you to be.  This primer on significant digits gives you basic information you will need to know for this class.

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They are the number of digits reported that do not include zeroes used only as "placeholders".  Placeholders are numbers used to indicate only the position of a decimal.

For example, in the number 0.01230, there are two placeholder zeroes: the first zero, which simply highlights the existence of the decimal, and the second zero, which indicates that the decimal is located one digit to the left of the "1".  One can tell that the first and second zeroes in this example must be decimal placeholders because the number 0.01230 can be re-written in scientific notation as 1.230 x 10^-1.

Notice that the last zero in 0.01230 is NOT a placeholder.  It serves no function in defining the position of the decimal.  It's presence in the number indicates that UNLIKE the other zeroes, this particular zero is a significant digit.

So, counting up the number of digits in 0.01230 that are not placeholders, there are 4 significant digits.
 
 

In the three examples given in the table above, the number of significant digits shown implies that the author made measurements to an accuracy NO GREATER THAN three, two, and five digits, respectively.  Typically the last significant digit is considered somewhat uncertain.  With this standard, the second number could be easily 1400, 1600, or possibly even 1900 or 1000.  This is in contrast to the last example in the table which implies that the actual number is 1500 give or take of no more than one.  Much more careful measurement is implied by the third number compared to the second number in the table.
 
 

As far as this class is concerned, one practical reason is that I will give full credit only to answers that give the number of digits I ask for.  Another reason is that it gives you an indication of how accurate you should strive to be.  You don't need to waste time trying to be more careful than you need to be.  But in the larger scheme of things, it is important for you to bear in mind how good numbers are and what they are really telling you.  For instance, most polls of the presidential election in 2004 had errors that indicated that George Bush and John Kerry were essentially tied.  A lot was made by pundits about "momentum" and such in these poll numbers, but the fact is, the measurements weren't good enough to show who would win.  The number of significant digits in these polls is, at best, two.  The poll numbers were correctly shown with two digits with the understanding that the second digit is somewhat uncertain. The same information can be more precisely obtained by looking at the estimated errors or uncertainties for the poll numbers. As we now know, Bush won but his margin was pretty small.