1.3 Accuracy, precision, and significant figures  (Page 3/12)

Percent uncertainty

One method of expressing uncertainty is as a percent of the measured value. If a measurement $A$ is expressed with uncertainty, $\mathrm{\delta A}$ , the percent uncertainty    (%unc) is defined to be

Uncertainties in calculations

There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its length and width has an uncertainty because the length and width have uncertainties. How big is the uncertainty in something you calculate by multiplication or division? If the measurements going into the calculation have small uncertainties (a few percent or less), then the method of adding percents    can be used for multiplication or division. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation . For example, if a floor has a length of $4\text{.}\text{00}\text{m}$ and a width of $3\text{.}\text{00}\text{m}$ , with uncertainties of $\mathrm{2\%}$ and $\mathrm{1\%}$ , respectively, then the area of the floor is $\text{12}\text{.}0{\text{m}}^2$ and has an uncertainty of $\mathrm{3\%}$ . (Expressed as an area this is $0\text{.}\text{36}{\text{m}}^2$ , which we round to $0\text{.}4{\text{m}}^2$ since the area of the floor is given to a tenth of a square meter.)

Precision of measuring tools and significant figures

An important factor in the accuracy and precision of measurements involves the precision of the measuring tool. In general, a precise measuring tool is one that can measure values in very small increments. For example, a standard ruler can measure length to the nearest millimeter, while a caliper can measure length to the nearest 0.01 millimeter. The caliper is a more precise measuring tool because it can measure extremely small differences in length. The more precise the measuring tool, the more precise and accurate the measurements can be.