Question F11 from 6th edition

[ChathuriGunasekera1D]

Hello! I am struggling to finish the last steps of this problem:

"The mass percentage composition of cryolite, a compound used in the production of aluminum, is 32.79% Na, 13.02% Al, and 54.19% F."

I am asked to find the empirical formula. I am fine up until after I have divided the three values by the smallest one, I don't know what I should multiply the values by. Thank you for any and all help!

[Vy Lu 2B]

I did the math and I got about 2.957 for the Na subscript and about 5.910 for the F subscript; I think you would be able to round off to the nearest whole number so that Na has a subscript of 3 and F has a subscript of 6? Does anyone agree with this? Unless you multiply everything by 1000 so that they're all whole numbers: Na2957Al1000F5910... sorry I began trying to help but I got confused too.

[ChathuriGunasekera1D]

Thank you! I think I rounded a little bit too much so my values weren't as close to a whole number.

[Gillian Ward 1F]

After I divided the three values by the smallest, I found the subscript of Na to be 2.9548, Al to be 1, and F to be 5.910. Since they're very close to a whole number, I just rounded up and got the empirical formula of Na3AlF6. It would be more obvious if the values needed to be multiplied to something to reach a whole number (for example, if you had 1.33 you would want to multiply everything by 3 to get 3.99 which would make the subscript 4). Hope this helps!