# Can someone lend me a hand in explaining sig figs involving different units?

## How would I solve and express the answer in sig figs?

Sep 28, 2016

You multiplied two answers, and one of them has three sig figs. The other has two. So the fewest number of sig figs indicates the number you are less sure about with regards to its precision.

$5.50 \times {10}^{8} \cancel{\text{mg")xx(4.0xx10^5 "mol")/(cancel"1 mg}}$

$= 2.2 \times {10}^{13} \text{mols}$

You only get the same number of sig figs from a multiplication or division process as the number you use with the fewest number of sig figs.

You can only be as sure as that which you are least sure about, which is the $4.0 \times {10}^{5} \text{mols}$, which only has two sig figs.

In your conversion factor, when you have "per . . . ", that is an exact relationship except for the larger number.

So if you have $\text{0.9464 L"/"quart}$, the $\text{L}$ is not exact, but the $\text{quart}$ is, because you're sure that for every quart, there is some quantity of $\text{L}$ that you are using fewer decimal places for than the exact value. Your estimate is based on what number you equate to a single unit of something else, and that would affect your sig figs.

Therefore, you have two sig figs, not one.