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Uncertainty in Measurement

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Accuracy - definition

Accuracy refers to the closeness of a measured value to a standard or known value. For example, if in lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then your measurement is not accurate. In this case your measurement is not close to the known value.

Precision - definition

Precision refers to the closeness of two or more measurements to each other. Using the example above, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise. Precision is independent of accuracy. You can be very precise but inaccurate, as described above. You can also be accurate but imprecise.
For example, if on average, your measurements for a given substance are close to the known value, but the measurements are far from each other, then you have accuracy without precision.

Significant figures - definition

Number of digits in a figure that express the precision of a measurement instead of its magnitude. The easiest method to determine significant digits is done by first determining whether or not a number has a decimal point.

Rules for determining the number of significant figures - definition

  1. All nonzero digits are significant.
  2. Zeros are also significant with two exceptions:
    • zeros preceding the decimal point.
    • zeros following the decimal point and preceding the first nonzero digit.
  3. Terminal zeros preceding the decimal point in amounts greater than one is an ambiguous case.

Questions on significant figures - example

Round off 92.810445 to three significant figures. In 92.810445, 928 are the first three digits, the next figure 1 which is less than 5, so we round off the number. When we round off 92.810576 to 3 significant figure is 92.8.

Related Concepts

Dimensional Analysis