# Rules for Counting Significant Figures

Continuing on from my previous post on Significant Figures, here I will go over some of the general rules. The rules that help us identify a sig fig are not difficult, and there are not many... but they are very important to understand. As always, understanding the basics is absolutely essential to being able to move forward.

As I mentioned previously, you DO NOT count a zero as a sig fig if it starts the number.
0.1 has 1 sig fig
0.0045 has 2 sig figs

All non-zero digits ARE significant.
123 has 3 sig figs
0.007654 has 4 sig figs

A zero that is found between other non-zero digits DOES count as significant.
101 has 3 sig figs
0.3056 has 4 sig figs

Numbers with a zero at the end MAY count it as significant. The distinction is whether the number contains a decimal place. If it does, then a zero at the end DOES count as significant. If there is no decimal place, then a zero at the end does NOT count as significant.
100 has 1 sig fig
100.0 has 4 sig figs
100. has 3 sig figs
50.30 has 4 sig figs
2.03000 has 6 sig figs
0.0098700 has 5 sig figs
9,885,000 has 4 sig figs

As I mentioned, the number of significant figures is often a result of the degree of precision in a measurement. However, sometimes the value must be taken in context to find the correct number of sig figs. For example, look at the number 100 above. I said it has 1 sig fig. However, if we are talking about a count of something... say, the number of houses on a street, then that value is precise to 3 digits, and it would be fair to say that, in this case, it would have 3 sig figs. Sometimes, this can be noted with a decimal point at the end, without any extra zeros (100.).

And those are all the rules for counting Significant Figures. They're not difficult once you practice for a while and recognize where the various rules apply.

Now that we have figured out just what counts as a sig fig, the next step is being able to do math with them... add them, multiply them, etc... and to do that, of course, we have an entirely different set of rules. This is the part that ALWAYS confuses people, so I will do my best to lay it out for you so that it makes sense.