So, 'bc' just has the (big) rationals. Rationals are the numbers you could make by taking one integer (say 5 or minus sixteen trillion and fifty-one) and dividing it by some positive integer (such as three or sixty-two thousand)

If we have a "Big Integer" type which can represent arbitrarily huge integers, such 10 to the power 5000, we can use two of these to make a Big Rational, and so that's what bc has.

But the rationals aren't enough for all the features on your calculator. What's the square root of ten ? How about the square root of 40 ? Now, multiply those together. The correct answer is 20. Not 20.00000000000000001 but exactly 20.