Question

Tom is trying to write 3/47 as a decimal.

He used long division and divided until he got the number 0.0638297872,at which point he stopped. Since the decimal doesn't seem to terminate or repeat, he concluded that 3/47 is not rational. Do you agree of disagree? Why?

Answer 1

Disagree. A rational number is any number that can be written as a fraction of two integers. Tom wrote 3/47, and both 3 and 47 are integers. Just because the decimal has not yet terminated doesn’t mean that the number he is looking at is irrational.