Like most things in science, significant figures have rules. The STAAR Chemistry Reference Materials document lists the rules for significant figure in a section titled, Rules For Significant Figures.

1. Non-zero digits and zeros between non-zero digits are always significant.
2. Leading zeros are not significant.
3. Zeros to the right of all non-zero digits are only significant if a decimal point is shown.
4. For values written in scientific notation, the digits in the coefficient are significant.
5. In a common logarithm, there are as many digits after the decimal point as there are significant figures in the original number.

Let’s look at these rules one at a time and see some examples.

Rule 1: Non-zero digits and zeros between non-zero digits are always significant.
This rule has two parts. Let’s look at each part.

Part A: Non-zero digits are always significant.
This is the easiest rule. This rule simply means that all numbers that are not zero (1, 2, 3, 4, 5, 6, 7, 8, and 9) are always significant. The number 56.7 has 3 significant digits.

How many significant figures are in the following measurements? Enter your answer into the box next to the measurement.

Part B: Zeros between non-zero digits are always significant.
If a zero falls between two non-zero numbers, it is significant. If you had a measurement of 805.74, you know 8, 5, 7, and 4 are significant based on Part A of Rule 1. The zero is also significant because it falls between two non-zero digits. So, 805.74 would have 5 significant figures.

How many significant figures are in the following measurements? Enter your answer into the box next to the measurement.

Rule 2: Leading zeros are not significant.
Leading zeros are zeros that are “place holders.” The number 0.69 has a leading zero in the ones place. The 6 and the 9 are significant. So, 0.69 has two significant figures. The measurement .000156nm has three significant figures.

How many significant figures are in the following measurements? Enter your answer into the box next to the measurement.

Rule 3: Zeros to the right of all non-zero digits are only significant if a decimal point is shown.
These zeros are sometimes called trailing zeros because they come after (or to the right of) non-zero numbers. There are three different scenarios with trailing digits.

Scenario 1- there are trailing zeros in a whole number and there is no decimal present
When there are trailing zeros in a whole number, and there is not a decimal, these zeros are not significant. An example of this would be the measurement 5900000 grams. Since there is no decimal point in this measurement, there would be only two significant figures, the 5, and the 9.

Scenario 2- there are trailing zeros to the right of the decimal
Trailing zeros to the right of a decimal are significant. An example of this would be the measurement 165.00 mL. In this measurement, the two trailing zeros are significant because there is a decimal shown.

Scenario 3- there are trailing zeros in a whole number and there is a decimal present
If there are trailing zeros in a whole number, and there is a decimal shown, then the zeros are significant. For example, the measurement 750.grams would have three significant zeros because of the decimal.

How many significant figures are in the following measurements? Enter your answer into the box next to the measurement.

Rule 4: For values written in scientific notation, the digits in the coefficients are significant.
Scientific notation was discussed in the previous lesson of this module. Remember, a number expressed in scientific notation has two parts: the coefficient and 10 raised to a power. The measurement 6.40 × 10^-3 moles would have three significant figures.

How many significant figures are in the following measurements? Enter your answer into the box next to the measurement.

Rule 5: In a common logarithm, there are as many digits after the decimal point as there are significant figures in the original number.
A logarithm has two parts that are separated by a decimal. The digits before (to the left of) the decimal are called the characteristic, and the digits after (to the right of) the decimal are the mantissa. According to Rule 5, there should be as many digits in the mantissa as there are significant figures in the original number. Let’s look at an example.

log(2.43 × 10¹) has three significant digits. When you calculate the logarithm, you will get the following:

1.386

Notice that the original number had three significant figures and there are three digits in the mantissa. Since only the numbers in the mantissa are significant, this value only has three significant figures.

Rules Review!

Watch this video to review the rules of significant figures that deal with zeros.