Why do we report uncertainties in measurements?

We report uncertainties in measurements to indicate the range of possible values for the measured quantity.

Measurements are never exact due to limitations in the measuring instruments and the methods used. Uncertainties are the range of values within which the true value of the quantity being measured is likely to lie. Reporting uncertainties is important because it allows others to understand the limitations of the measurement and to compare it with other measurements.

There are two types of uncertainties: random and systematic. Random uncertainties arise from the limitations of the measuring instrument and the method used. They can be reduced by taking multiple measurements and calculating the standard deviation. Systematic uncertainties arise from a flaw in the measuring instrument or method and can only be reduced by improving the instrument or method.

Uncertainties are reported using the following format: measured value ± uncertainty. The uncertainty is usually expressed as a percentage of the measured value. For example, if the measured value is 10.0 ± 0.1 cm, the uncertainty is 1%. The uncertainty can also be expressed as a range of values, such as 9.9 cm to 10.1 cm.

In conclusion, reporting uncertainties in measurements is important because it allows others to understand the limitations of the measurement and to compare it with other measurements. Uncertainties can be random or systematic and are reported using a specific format.