Question

Is `1.bar4` rational or irrational?

Answer 1

Read below.

Explanation:

In a real number system, you could define two groups: the irrationals and rationals.

Irrationals are decimals that do not terminate (doesn't end), doesn't have a pattern, and cannot be expressed into a fraction of `a/b` where `a` and `b` are integers and `b!=0`.

When a number is real and it is not an irrational, it is automatically a rational.
`1.bar4` is a decimal that has a pattern(the `4` goes on forever.)

Therefore, it is a real and a rational number.