# Question #8654e

Jul 20, 2015

A result is rounded off because it has to match the number of sig figs used in the measurements/calculations.

#### Explanation:

First of all, significant figures have nothing to do with accuracy, they are related to precision.

The greater the number of sig figs you use in a measurement, the greater the precision of the measurement. The accuracy depends on whether or not the device you used was calibrated properly.

So, results are always rounded off to match the values given with the smallest number of sig figs. Simply put, your result cannot have a precision that exceeds that of your least precise measurement.

So, let's that you want to figure out the density of a piece of metal. You weight the metal and find that it has a mass of 100 g. The scale you use has a precision of only one sig fig.

Now you use a cylinder that contains water to measure its volume. You work out the volume to be 50.235 mL.

When you calculate density, you have to divide these two values

$\rho = \frac{m}{V} = \text{100 g"/"45.235 mL" = "2.21068 g/mL}$

You have to round this off to one sig fig, since that represents the less precise measurement.

You have to do that because the scale you used was not very precise, meaning that those 100 g could just as well be 105, 99.8, 121.225, etc.

This means that the density of the metal has to be given as

$\rho = \text{2 g/mL}$

This reflects how the poor precision used when measuring the mass of the sample affects the high precision used when measuring the volume.

Remember, poor precision always beats high precision - and the number of sig figs you use must be a clear reflection of this!