# Question 93106

Feb 10, 2018

We have no way of telling...

#### Explanation:

I think it's safe to say that your question is incomplete, but my guess is that you're dealing with a stoichiometry problem that involves the conversion of a number of atoms of zinc to moles.

Avogadro's constant, which is usually given as $6.02 \cdot {10}^{23}$, has three significant figures because that's how many sig figs you have in the mantissa of the number.

$6.02 \text{ "->" " "3 sig figs: } \left\{6 , 0 , 2\right\}$

As a side note, you usually don't have to worry about the number of sig figs you have for Avogadro's constant because you can use constants with as many significant figures as you need in your calculations.

So, for example, if you have a sample of zinc that contains $2.76 \cdot {10}^{24}$ atoms of zinc. Once again, you can say that this number has three significant figures because you have

$2.76 \text{ " ->" " "3 sig figs: } \left\{2 , 7 , 6\right\}$

you can find the number of moles present in the sample by using Avogadro's constant as a conversion factor.

2.76 * 10^(24) color(red)(cancel(color(black)("atoms Zn"))) * "1 mole Zn"/(6.02 * 10^(23)color(red)(cancel(color(black)("atoms Zn")))) = "4.5847 moles Zn"#

Now, because the number of atoms of zinc and Avogadro's constant have three significant figures and because you are multiplying the two values, the answer must be rounded to three significant figures as well.

So you must report

$\text{4.5847 moles Zn " ~~ " 4.58 moles Zn}$

as the answer. The fact that the number of moles is $< 10$ must have something to do with the fact actual problem.