This problem demonstrates a particular problem: how do you know when to round off a value to the nearest whole number? This is a problem because there are problems where rounding off too early would be a mistake. Generally, the only way to know is by experience.

Problem: A compound containing only carbon, hydrogen and oxygen is found to be 48.38% carbon and 8.12% hydrogen by mass. What is its empirical formula?

Step One: percent to mass.

Carbon: 48.38 g
Hydrogen: 8.12 g
Oxygen: 100 minus (48.38 + 8.12) = 43.50 g

Step Two: mass to moles.

Carbon: 48.38 g ÷ 12.011 g/mol = 4.03 mol
Hydrogen: 8.12 g ÷ 1.008 g/mol = 8.04 mol
Oxygen: 43.50 g ÷ 15.999 g/mol = 2.72 mol

Her is where the problem with rounding comes into play. Should the 2.72 be rounded off or not? If you do, then the answer is C4H8O3. Is it right or wrong? Let us continue.

Step Three: divide by small.

Carbon: 4.03 mol ÷ 2.72 mol = 1.48
Hydrogen: 8.04 mol ÷ 2.72 mol = 2.96
Oxygen: 2.72 mol ÷ 2.72 mol = 1

Step Three: multiply 'til whole.

Doubling each value gives C = 3, H = 6, O = 2, so the empirical formula is C3H6O2.

Notice that we rounded off 1.48 and 2.96 in step three. These amounts of rounding off introduce much less error than rounding off 2.72.

So how do you know? Sorry, there is no hard and fast rule. You must make ajudgement call based on experience. The above problem has tried to give you some experience.