Question

suppose that a number written as a decimal has an infinite number of non- repeating digits after the decimal point. What is this number called

Answer 1

Answer: Irrational number

If the decimal digits repeat forever, then the repeating decimal is considered rational.

For instance, 2/99 = 0.020202020202... where the "02" repeats forever

If we don't have such a pattern, then we cannot write the decimal as a fraction of two integers and the number is not rational. So it is irrational.