Usage of decimal expansion

Question

I learned about the rigorous construction of rationals as a set of equivalence classes of ordered integers with operations defined on this set. I understand that the decimal expansion is another way to represent the same rational as the sum of other rationals. There happen to be rationals with repeating decimal expansions. What bothers me is why is this decimal expansion representation of a rational number is used by people when we have a careful constructed rational number system? When we represent a number with repeating digit in computers we have to give it a finite decimal expansion thus obtaining a different number compared to the one we wanted to represent. For example if we have 1 thing(that can be divided in 60 equal parts) and we want to divide it in equal parts(suppose 3), when we use rational number system as constructed we get 20 as result. But what if we wanted to use decimal expansion to calculate the same thing? Then 0.33(for example) multiplied by 60 gives 19.8 which is not equal to 20. Then why people saw something good in this decimal expansion representation of rational numbers and constantly use it? Am I missing something?

Answer 1

"Then why people saw something good in this decimal expansion representation of rational numbers and constantly use it?"

One reason is that it's easy to add decimal numbers, but to add two fractions you have to find a common denominator. Consider calculating $${1\over5}+{1\over7}+{1\over8}+{1\over9}+{1\over11}+{1\over13}$$ by finding a common denominator, and see what large numbers emerge, even though all the numbers in the problems are small. Compare that to doing it using decimals.