Question

18. Tom is trying to write as a decimal. He used long division and divided

until he got the quotient 0.0638297872, at which point he stopped. Since
the decimal doesn't seem to terminate or repeat he concluded that is
not rational. Do you agree or disagree? Why?

Answer 1

disagree; long division gives the result of computing the ratio of integers--a rational number

Explanation:

If Tom is dividing one integer by another, he already knows the value is rational. (A rational number is the ratio of two integers.)

It appears Tom's number is 3/47, which has a 46-digit repeating decimal fraction. Tom will not see the repeat unless he continues way beyond the 10 digits he has computed so far.