# How do you calculate the following to the correct number of significant figures?

## a) $\frac{1.27 g}{5.296 m L}$ b) $\frac{12.235 g}{1.01 L}$ c) $\frac{17.3 g + 2.785 g}{30.20 m L}$

Oct 2, 2016

a)$0.240 \frac{g}{m L}$

b)$12.1 \frac{g}{L}$

c)$0.666 \frac{g}{m L}$

#### Explanation:

When dividing, the quotient should have the same number of significant figures as the smaller number of sig figs in either the dividend or divisor.

When adding, the sum should have the same number of signficant figures as the "least accurate" place in the addends.

a) $\frac{1.27 g}{5.296 m L} = 0.2398 \frac{g}{m L}$

which I will round to $0.240 \frac{g}{m L}$ because $1.27$ has only 3 significant figures.

b)$\frac{12.235 g}{1.01 L} = \frac{12.114 g}{L}$

which I will round to $12.1 \frac{g}{L}$ because $1.01$ has only 3 sig figs.

c)$\frac{17.3 g + 2.785 g}{30.20 m L}$

First add the numbers in the numerator.

$17.3 + 2.785 = 20.085$ which I will round to $20.1$ because the "least accurate" place in either of the addends is the tenths place in $17.3$

Next, complete the division.

$\frac{20.1 g}{30.20 m L} = 0.6656 \frac{g}{m L}$

which I will round to $0.666 \frac{g}{m L}$ because $20.1$ has only 3 sig figs.