Rules for determining the number of significant figures
From Chemistry Resource
| RULES: | (Significant figures are the figures in red) | |
|---|---|---|
| Rule 1. All nonzero integers are significant. | eg - 456 cm | 456 cm has 3 significant figures |
| Rule 2. All zeros to the left of the first nonzero digit are not significant since they are used to locate the decimal point. | eg - 0.00567 kg | 0.00567 kg has 3 significant figures |
| Rule 3. All zeros between nonzero digits are significant. | eg 1 - 207.08 cm eg 2 - 0.0401 L |
207.08 cm has 5 significant figures 0.0401 L has 3 significant figures |
| Rule 4. All zeros at the end of a number that has a decimal point are significant. | eg 1 - 34.070 mg | 34.070 mg has 5 significant figures |
| eg 2 - 0.0670 g | 0.0670 g has 3 significant figures | |
| eg 3 - 400. mm | 400. mm has 3 significant figures | |
| Rule 5. Zeros at the end of a whole number that has no decimal point is confusing since they may or may not be significant. | eg - 300 L | ??????? The measurement, "300 L", as written is confusing. |
Why is the writing a measurement such as "300 L" confusing?
This measurement, as written, ends with zeros but it does not have a decimal point. This leads to confusion because it is not certain whether this measurement is
- measured using a bucket such that the volume can be anywhere between 250 L to 350 L. In this case, then 300 L has 1 significant figure.
- measured using a measuring device such that the volume is measured to the nearest ten liter, then the measurement is accurate to within 295 L to 305 L. In this case, then 300 L has 2 significant figures.
- measured using a more accurate measuring device such that the volume is measured to the nearest liter, then the measurement is accurate to within 299.5 L to 300.5 L. In this case, then 300 L has 3 significant figures.
To remove the ambiguity associated with any written measurements, we need to be more clear in the way we represent the measurement of "300 L". We can do this in two ways:
- using scientific notation (the recommended way)
- using an overbar to indicate that any figures written to the right of the digit with the overbar is not a significant figure.
| To represent "300 L" as a measurement with | Scientific Notation (recommended) |
Overbar Notation |
| 1 significant figure | 3 x 102 L | 
|
| 2 significant figures | 3.0 x 102 L | 
|
| 3 significant figures | 3.00 x 102 L | 
|
Never leave the measurement written as "300 L" !!!
[Having said that, most likely the interpretation of the measurement recorded will be 1 significant figure.]
Content suitability
BCIT courses: CHEM 0011
