Significant figures
Except for numbers which are exact numbers or counting numbers, it is often impossible to determine an exact value of a quantity that is under investigation. In section 1.5, we saw that in all experimental measurements, there is a degree of uncertainty.
When a scientist takes a measurement there are three kinds of information that are recorded:
- The magnitude of the measurement.
- The reliability of the number.
- The unit of the measurement.
The magnitude and reliability of the measurement
Since all experimental measurements have uncertainties, we need to know how much we can trust the measurements. Let's illustrate the idea by considering the mass of an object measured on two different balances. Assuming that the two balances are accurately calibrated, let's take one measurement on a "crude" balance, and take the other on a "sophisticated" balance.
The table below shows us how to interpret the two masses.
| crude balance | sophisticated balance | |
|---|---|---|
| Measurement | 12.4 g | 12.4536 g |
On a crude balance, we are able to measure to 1 decimal place. On a sophisticated balance, we are able to measure to 4 decimal places. The digits that have no uncertainty are the digits in blue. In other words, the digits that are in blue are the digits that are CERTAIN. The last digit of a measurement that is shown in red always carry an uncertainty due to estimation. The measured quantity, 12.4536 g, is a more accurate mass than 12.4 g because the mass of the object is known to the ten-thousandth decimal place.
In scientific work, we must always be careful to write down the quantity of measurements properly and to report and calculate quantities that reflect on the accuracy of the measurements. For these reasons, it is important to indicate the margin of error in a measurement by clearly indicating the number of significant figures.
We can determine the number of significant figures for any measurement.
# of sig fig = # of digits that are CERTAIN + 1 final uncertain digit
Points to note:
- 12.4539 g is a measurement with 6 significant figures. (All digits except for the the final digit '9' are CERTAIN. The final digit '9' is the uncertain digit.)
- 12.4 g is a measurement with 3 significant figures. (All digits except for the the final digit '4' are CERTAIN. The final digit '4' is the uncertain digit.)
Given that the measuring tool is correctly calibrated, in general, a measurement that has more significant figures is the more accurate or reliable measurement.
Content suitability
BCIT courses: CHEM 0011
