Significant Figures

In the same way that speakers use word choice to indicate the reliability of their numbers, scientists show the precision of their measuring devices in the way they write numbers, and the key to the system is the decimal point. 

The further to the right a number ends (relative to the decimal point) the more precise the number is. That means that 2.367 g is more precise than 45887.1 g. The first number comes from a device that measures to the nearest 1000^th of a gram while the second number is only measured to the nearest 10^th of a gram, and is therefore less precise. 

To determine how precise and reliable a number is you can do one of two things. (Actually, you need to be able to do both.) You need to be able to count decimal places and count significant figures. 

Decimal places are simply the number of digits to the right of the decimal point in a number. Thus 1.993 has three decimal places, 0.00004 has 5 decimal places and 387 has zero decimal places.

Significant figures are the digits in a number that report the reliability. It is this idea that makes 1,000,000 when described as “like a million” different from the number 1,000,000 when described as a counted quantity. 

Significant figures are trickier to count than decimal places, because they can be both before and/or after the decimal point and they depend on the decimal point and on the placement of non-zero numbers. 

You should understand that significant in this context does NOT mean important and non-significant does NOT mean unimportant. Significant means only that the digit in question is probably a reliable digit and not only a place holder.

 

As an example, in the number 1,000,000 (when it means "like" a million) the zeros are not significant. That means that they are NOT telling us how reliable the number is. They are important (without them the number would be 1 -- a very different quantity and not at all "like" a million) but they are not significant. The choice of words is unfortunate but, alas, it is older than all of us and we're stuck with it. 

Now that you understand the idea behind significant figures, you need to understand how to recognize significant figures in a number.