Uncertainty in Measurement

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When dealing with objects that can be counted, one can always get an exact answer. But while measuring the weight of a person, the volume of milk in a container, the length of a cloth etc. it is not possible to measure them exactly. The difference in the two situations arises because objects are measured by a discrete (distinct) variable (there can be three or four balls and nothing in between) while quantities like weight, volume etc. are measured by a continuous variable (weight can be 42kg or 43kg or anything in between). Measurement of continuous variable can only be as precise as the skill of the observer and the choice of the measuring apparatus. The limit of reproducibility of any measurement is known as its precision. A measurement may be absolutely precise or uncertain depending upon the instrument or the person making the measurement. The degree of conformity of a measure to its true value is termed as its accuracy.

Skill and Accuracy of the Observer

Suppose three students A, B and C measure the volume of the liquid in a cylinder. They report the following values:

Result of A: 23.4 mL; Result of B= 23.5 mL; Result of C= 23.6 mL

If the correct volume of the liquid is 23.5 mL, it means that the student B has measured the volume of the liquid correctly while the students A and C have made some error.

Limitation of the Measuring Instrument

Limitation of the measuring instrument is an important factor. This leads to uncertainty in measurement. In order to understand this, let us assume that we want to measure the volume of the liquid with a graduated cylinder. If the volume of the liquid is more than 23 mL and less than 24 mL, it lies between 23 and 24 mL.

With the scale on the measuring cylinder, one cannot have a correct reading in the first decimal place. We can guess that it is approximately in the middle of 23 and 24 and therefore, the volume of the liquid may be reported as 23.5 mL. Here 2 and 3 are certain digits while 5 is an uncertain digit. Therefore, different persons measuring the volume of the liquid might report volumes that differ by 0.1 or 0.2 mL. So, every scientific measurement has some degree of uncertainty. This is mainly due to the skill of the observer and limitation of the instrument. This uncertainty of measurement is expressed in figures called significant figures.