In chemistry (like in most other fields!) we concern ourself with the size of that plus/minus interval. Just how big it is will determine how many significant digits there are in a result.
For example, when someone writes 4.5332 g they are implying that the number of grams is known to +/- 0.0001 gram. If that mass were to be compared to another mass of say 43.23 g (which as written is implied to be known to +/- 0.01 g) we would say that the uncertainty in the second mass is larger than in the first. So there would be no point in reporting the sum of the two masses to any smaller uncertainty than +/- 0.01 g. So claiming that the sum was 47.7632 g (+/- 0.01 g) would be silly since the last two digits obviously have no meaning. The correct way of reporting the sum would be to round the result to the correct uncertainty of +/- 0.01 g.
| Rule: | When adding or subtracting values, always retain the largest uncertainty in the result. |
Here is an example.
| Example: | A beaker is weighed and found to have a mass of 78.45 g. A sample of sodium chloride is added to the beaker and the beaker is weighed again using a different balance. The NaCl plus the beaker are found to have a mass of 79.6743 g. What is the mass of the sodium chloride? |
| Solution: |
First, take the difference to get the mass of the sodium chloride:
79.7643 g (mass of beaker and NaCl)
- 78.45 g - (mass of beaker )
--------- -------------------------
3.3143 g (mass of NaCl)
Next, round to the correct number of significant digits:
3.3143 g ==> 3.31 g
|
| Note: We can retain only those decimal places that the uncertainty allows. In this case, +/- 0.01 g for the mass of the beaker meant we needed to round to the nearest hundredth of a gram. | |