Accuracy refers to how closely a measured value agrees with the correct value.
Precision refers to how closely individual measurements agree with each other.
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Let’s look at an example where significant figures is important: measuring volume in the laboratory. This can be done in many ways: using
A rule of thumb: read the volume to 1/10 or 0.1 of the smallest division. (This rule applies to any measurement.) This means that the error in reading (called the reading error) is 1/10 or 0.1 of the smallest division on the glassware. If you are less sure of yourself, you can read to 1/5 or 0.2 of the smallest division.
Conclusion: The number of significant figures is directly linked to a measurement. If a person needed only a rough estimate of volume, the beaker volume is satisfactory (2 significant figures), otherwise one should use the graduated cylinder (3 significant figures) or better yet, the buret (4 significant figures).
So, does the concept of significant figures deal with precision or accuracy? Hopefully, you can see that it really deals with precision only. Consider measuring the length of a metal rod several times with a ruler. You will get essentially the same measurement over and over again with a small reading error equal to about 1/10 of the smallest division on the ruler. You have determined the length with high precision. However, you don’t know if the ruler was accurate to begin with. Perhaps it was a plastic ruler left in the hot Texas sun and was stretched. You don’t know the accuracy of your measuring device unless you calibrate it, i.e. compare it against a ruler you knew was accurate. Note: in the laboratory, a good analytical chemist always calibrates her volumetric glassware before using it by weighing a known volume of liquid dispensed from the glassware. By dividing the mass of the liquid by its density, she can determine the actual volume and hence the accuracy of the glassware.
