What are the reasons for using significant figures in equations?

I'm home schooled and I'm taking physics, anyway it gives an example of a ruler capable of measure to the nearest tenth, measuring the width and length of a square. Then it uses the equation, width * length, to calculate the area of the square. When you multiply 5.8 cm x 1.4 cm you get 8.12 cm, but it says that you should only present it as 8.1 because the ruler is only capable of measuring to the nearest tenth- that might be true, but in an equation it isn't even capable of that. What if the real measurements where something like 5.89 and 1.49, then the answer would be 8.7761; in equations its not even capable of being accurate to the nearest tenth. So 8.12 is closer to the actual answer than 8.1 is. And if the reason for shortening the answer is to show how accurate the ruler is, why don't they have some sort of system, like underlining the numbers of the answer that the ruler can measure accurately to. I don't understand, can someone elucidate - thanks.