In the sciences, not just chemistry, it is important to honestly convey how accurate a certain measurement is. We have a lot of different ways we convey this, but one of the most important is significant figures, which you will often hear shortened to “sig figs.”

To understand the importance of significant figures, we need to understand the two different types of values that we encounter in science. The first type are exact values. One example of an exact value would be a counted value. For example, if you count and see that there are 17 students in a class, that is an exact value. The value doesn’t just lie somewhere between 16.9 and 17.1. It is exactly 17. Another way you will encounter exact values is definitions. For example, 12 inches is defined as 1 foot, that’s not an estimation, that is exact.

Outside of exact values, the other type of value that we encounter far more often are measured values. Any time a value is measured, there is going to be a certain amount of estimation or rounding, because no measurement instrument is perfect. We don’t ever need to worry about sig figs when we are dealing with exact values, but when we are dealing with measured values, they are critical.

The first rule for determining the number of sig figs is digits 1 through 9 are always significant. For example, if you are given the measurement 77.2 kilometers, all three of those digits are significant. Thus, this value has 3 significant figures.

The next rule, when determining how many sig figs a measurement has, is that zeros in the middle of a number, called “included zeros,” are always significant. For example, with the value 94.072 grams, each digit, including the zero in the middle, is significant. Thus, this value has 5 sig figs.

Next, rule 3 tells us that zeros that are at the beginning of a number, often called leading zeros, are never significant. For example, the measurement 0.0834 centimeters has two leading zeros. The leading zeros are not significant, but the 3 digits after them are. Thus this value has 3 sig figs.

Rule 4 tells us that the zeros at the end of a number AND after the decimal point are significant. For example, this measurement of 138.200 meters has two zeros at the end, that also occur after the decimal point. These zeros are all significant because they are necessary to show the accuracy of the measurement. This measurement is accurate to the thousandth of a meter, but if we drop those zeros off, the reader wouldn’t know that. So this measurement has 6 sig figs.

The last rule is the trickiest. This rule tells us that the zeros at the end of a number and before an implied decimal point may or may not be significant. In order to know whether or not the trailing zeros are significant, the writer has to give a little more information. There are a couple ways to show whether or not trailing zeros are significant. The first way is to just write the number of sig figs next to the value. For example, you may see a measurement like this: 125,000 kilograms, and next to that value the author put 4 SF in parentheses. That means that the first 4 digits are all significant, even though one of them is a trailing zero. So with this measurement, the zero in the hundreds place is significant, but the ones in the tens and ones places aren’t.

One other method you may see used is for the writer to put a decimal at the end of a number. For example, the value 9100 kilograms looks like it is only accurate to the hundreds place, but that decimal tells us that all of the digits are significant, and that this measurement is actually accurate to the ones place. So this value has 4 significant figures.

Significant figures can be tricky to figure out, but even though they are challenging, they are very useful. We will see just how important sig figs are as we begin using these measured values to perform calculations.