The number of meaningful digits expressed in a numerical value is referred to as its number of significant figures, or sig figs for short. They are sometimes also referred to as significant digits or sig digs. To be both precise and accurate, yet facilitate calculation, experimental measurements are expressed using significant figures with the understanding that an uncertainty exists of ± one unit of the last reported digit.
For example, it is understood that 25 degrees C actually means 25 ± 1
degree C.
This number has two significant figures.
The value 25.5 degrees C means 25.5 ± 0.1 degree.
This number has three significant figures.
This eliminates the cumbersome need to express a ± value after every measurement and when showing calculations. The level of precision is simply implied by the number of significant figures expressed.
To determine how many significant digits a particular numerical value has, apply the following rules, in order. Remember, almost all of the the confusion about significant digits comes from figuring out which ZEROS are significant!
If a number is correctly expressed* in scientific notation, all the digits -- except the ones that are part of the exponent -- are significant. Ignore any digits that come after the E and count the rest.
| 1 x 10³ (1 e 3) | has one sig fig |
| 1.2 x 10⁻³ (1.2 e -3) | has two sig figs |
| 1.20 x 10⁵ (1.20 e 5) | has three sig figs |
| 1.02 x 10⁻⁷ (10.2 e -7) | has three sig figs |
| 1.020 x 10⁴ (1.020 e 4) | has four sig figs |
* On a test or quiz, but not in lab life, you might see a number written in scientific notation with some leading zeros, just to try to trip you up. Don’t count the leading zeros and do complain to the test writer!
| 1.2 x 10⁻³ (1.2 e -3) | has two sig figs |
| 01.2 x 10⁻³ (1.2 e -3) | has two sig figs |
| 001.2 x 10⁻³ (1.2 e -3) | has two sig figs |
If a number is written in scientific notation, just apply Rule 0 and be done.
HideALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant, regardless of decimal place location.
| 1234 m | has four sig figs |
| 1.234 ml | has four sig figs |
| .1234 g | has four sig figs |
| 1234. km | has four sig figs |
Zeros appearing to the left of (“in front of”) the first non-zero digit ARE NOT significant.
| 0.0009 g | has one sig fig |
| 0.045752 m | has five sig figs |
| 0.0056 kg | has two sig figs |
Check out the very last digit to the right. If it is non-zero, proceed to Rule 4.
| 45.0 g | has three sig figs |
| 450. g | has three sig figs |
| 450 g | has two sig figs |
ALL zeros sandwiched by (between) significant digits from Rules 1-3 are ALWAYS significant. Any zeros 'left outside the sig fig sandwich' ARE NOT significant.
| 60.3 L | has three sig figs |
| 93005 km | has five sig figs |
| 505 g | has three sig figs |
| 50500 g | has three sig figs |
| 50500. g | has five sig figs (Rules 1, 3, and 4) |