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### Empirical Formula

Posted: Tue Oct 02, 2018 7:19 pm
So I came across some problems on the modules that asked for empirical formulas and I was confused on how to get atoms to be a whole ratio.

For example, if a ratio is 1 : 0.13 : 2.23, in this case, how do we multiply to get the ratio to be whole numbers, do we just multiply until both decimals are relatively close to a whole number?

What number do I multiply by?

thank you!

### Re: Empirical Formula

Posted: Tue Oct 02, 2018 7:27 pm
The best way of approaching this is to try to multiply the decimals by the smallest number possible.

For example, we can either multiply based on the 0.13 or the 2.23.
0.13 is close to 0.10, so we would theoretically multiply all the numbers by 10.
2.23 is close to 2.25, so we would theoretically multiply all the numbers by 4.

4 is the smaller number, so multiply the three numbers by 4 to get 4 : 0.52 : 8.92.
Since the middle number is still a decimal, multiply once again (this time by 2, since 0.52 is close to 0.50).

I think the final ratio should be 8 : 1 : 18.

The only issue I'm not sure on is whether 8.92 is high enough to be rounded to 9. If someone else could shed some light on that, that would be great! :)

### Re: Empirical Formula

Posted: Tue Oct 02, 2018 8:17 pm
I think the general rule was that if you're going to round, the rounded number should be within 5% of the original answer you got.

### Re: Empirical Formula

Posted: Tue Oct 02, 2018 8:54 pm
I think you can just divide all the other bigger numbers by the smallest one and round them to by the significant figure rules. Cuz I think in this case, some roundoff is acceptable

### Re: Empirical Formula

Posted: Tue Oct 02, 2018 9:20 pm
In this case, another way of getting to that answer would be to take the smallest number in that ratio and divide all numbers within the ratio by that number. When you do that you get:
1/0.13= 7.7
0.13/0.13= 1
2.23/0.13=17.15
When rounded, the ratio will then be: 8:1:17

### Re: Empirical Formula

Posted: Wed Oct 03, 2018 10:44 pm
You would want to start off by dividing with the smallest number, then multiply all of the numbers by the same whole number to get the least whole number possible.