# Question #8654e

##### 1 Answer

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

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

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!