What is the Difference Between Precision vs Approximation?

What is the Difference Between Precision vs Approximation?

A term that people seem to misinterpret with precision is approximation. A fairly reasonable number of people believe that the reason for approximating a value is to make it precise. This is because people always think that precision translates into accuracy, and that when a value is approximate, you are making it more precise and thus accurate.

Although the definitions found in the dictionaries for these three terms are not entirely wrong, in STEM where these terms are very important, precision doesn’t mean accuracy, and approximation might not make a value accurate. Things might have started to get a bit confusing here, so now it will be good to define both terms. So what is the difference between precision and approximation? Let’s take them separately to better understand.

Definition of Precision

Precision is the proximity of a set of obtained results to each other. So what does this definition of precision say?

To begin with, precision is not synonymous with accuracy. A set of values might be precise, that is, very close to each other, and not accurate. Accuracy is the closeness of a value to a given true value. For example, during the course of a titration experiment, you performed four tests of the same sample and obtained 23.4, 23.2, 23.3 and 23.1. These results are proximal and hence precise, but when you calculated, you obtained an actual result of 29. This means your experimental values, although precise, aren’t accurate as they are very far from the exact result.

Precision might also mean giving an exact or more distinct detail about something, a measurement for example. Now this seems more obvious to you, doesn’t it? Measuring in millimetres gives a more precise result than in centimetres, just as taking measurements using a digital scale gives a much more distinct value than the analogue ones. Being precise in this sense might however lead to accuracy.

Definition of Approximation

Approximation simply means making a value with fewer digits or making the value simpler. When you round a number, you are making it shorter hence closer to the initial value. Also, when you make a calculation by omitting some factors affecting that particular phenomenon, for example air resistance when calculating the force of a moving body, you’ll get an approximate value, not the exact one. Now we can see that approximation is different from precision.

Like precision, approximation might also lead to accuracy.

From the definition of approximation and precision, we can make a comparison table to make their differences clearer.

Main Differences Between Precision vs Approximation

Precision Approximation
Precision is the closeness of a set of values to each other. Approximation is the simplification of a value.
Precision can also be the result of further measurement.Occurs when some factors affecting a result are omitted.
Usually of importance when conducting an experiment of physical measurement. Usually done in calculations, to simplify an answer.
Occurs when more than one value is involved or when there are differences in the calibration of measuring instruments. Usually occurs when a rational number e.g. is used in order to limit the answer to a specific significant figure.

Difference Between Precision and Approximation: Conclusion

In conclusion, as the definitions and vs. table show, precision and approximation are not the same and neither is exactly synonymous to accuracy. However, both can lead to accuracy. The difference should be clear by now.