Sig Fig: How Many Magnesium Ions in 200 kg MgO?

[STEMucator]

Homework Statement

A 200. kg sample of MgO is given (Notice 3 sig figs). How many kg of magnesium ions would there be?

Homework Equations

%Mg = 62%
%O = 38%

The Attempt at a Solution

Just a quick question I had about significant figures.

The sample of MgO given is 200.kg (3 sig figs). The percent composition of magnesium is 62% (2 sig figs). Therefore 62% of the 200.kg will be magnesium.

(62%/100%)(200.kg) = (0.62)(200.kg) = 124kg, but because the answer must have 2 sig figs, the final answer would be 120kg ( This is my suspicion ).

Notice if the kg of oxygen is calculated :

(38%/100%)(200.kg) = (0.38)(200.kg) = 76kg. This answer already has 2 sig figs, so nothing needs to be changed.

Now when added together : 120kg + 76kg = 196kg < 200.kg.

Is this result a fault of the rules or a fault of my own?

 

[Borek]

Is this result a fault of the rules or a fault of my own?

Rounding often messes the result in some way. And as significant digits are far from being perfect (generally speaking they are a poor man's way of dealing with uncertainties) there is nothing strange in the fact calculations done using them yield strange results.

 

[STEMucator]

Rounding often messes the result in some way. And as significant digits are far from being perfect (generally speaking they are a poor man's way of dealing with uncertainties) there is nothing strange in the fact calculations done using them yield strange results.

Yes, rounding leaves a sour taste every time. Thank you for the confirmation though, I just wanted to make sure.