When to know to multiply by a whole number when finding the empirical formula

[Kimberly Bauer 4E]

I'm doing Fundamentals F.11 letter B and I was dividing 31.91 K/30.0983 and it gave me 1.060. I found the rest of the calculations for the other elements and I ended up dividing each of the numbers by the smallest number which was 0.8160. I got 1.299 for K. When do I know when to multiply to find a whole number or is this number fine to round down and say 1?

[Osvaldo SanchezF -1H]

When finding the empirical formula, after you divide by the smallest number you kind of have to use your best judgment to determine whether you have to multiply by a whole number or not, and in most cases you do. Considering 1.299, would you believe it to be close to 1, well not really since it is around .29 off which is quite a difference if you think about it. So you would multiply it by a whole number like 3 to get 3.897. Now the difference to the next whole number is much less and determines it to be 4. Use your best judgment depending on the ratios! Btw you got the molar mass of K wrong because it is 39.1gmol^-1 and not what you put. I am sure that if you do it over again with the right moles for K, then you will find it easier to know what to do.

[Kimberly Bauer 4E]

When finding the empirical formula, after you divide by the smallest number you kind of have to use your best judgment to determine whether you have to multiply by a whole number or not, and in most cases you do. Considering 1.299, would you believe it to be close to 1, well not really since it is around .29 off which is quite a difference if you think about it. So you would multiply it by a whole number like 3 to get 3.897. Now the difference to the next whole number is much less and determines it to be 4. Use your best judgment depending on the ratios!

The solutions manual rounded it to 1 tho so that's why I was confused because I was also multiplying it by 3 /:

[Amy Kumar 1I]

Some of the common decimals are .25, .33, and .5 so in those cases, there is a clear way to multiply and make the quantity a whole number. Try to find a number you can multiply it too to get as close to a whole number as possible.

[Sean Sugai 4E]

I'm doing Fundamentals F.11 letter B and I was dividing 31.91 K/30.0983 and it gave me 1.060. I found the rest of the calculations for the other elements and I ended up dividing each of the numbers by the smallest number which was 0.8160. I got 1.299 for K. When do I know when to multiply to find a whole number or is this number fine to round down and say 1?

For K, the molar mass is 39.0983 g/mol, so instead of 1.060, it should be 0.816148 mol K, which would then be divided by 0.816. This would make it 1 instead of 1.299 for K.

As a general rule, however, you should multiply by a whole number when the value isn't ~0.1 away. For example, you should round 2.9 to 3 or 1.1 to 1. Instances such as 1.33 can be multiplied by 3 to round to 4 or 2.5 can be multiplied by 2 to get 5.

[Osvaldo SanchezF -1H]

When finding the empirical formula, after you divide by the smallest number you kind of have to use your best judgment to determine whether you have to multiply by a whole number or not, and in most cases you do. Considering 1.299, would you believe it to be close to 1, well not really since it is around .29 off which is quite a difference if you think about it. So you would multiply it by a whole number like 3 to get 3.897. Now the difference to the next whole number is much less and determines it to be 4. Use your best judgment depending on the ratios!

The solutions manual rounded it to 1 tho so that's why I was confused because I was also multiplying it by 3 /:

The problem was that you got the moles of K incorrect for the problem since you used the wrong molar mass. Fixing that you should get.816 mole of K and not 1.299. So when you divide by the smallest number, that being 0.816, you get 1 mole of K