Question

Is 0.375 rational or irrational?

Answer 1

Anything that can be expressed as a fraction with an integer numerator and an integer denominator is rational.

`0.375 = (375)/(1000)`
and is therefore rational.

Any number which when written as a decimal form which terminates (that is ends with only `0`-value digits following the last digit) or any decimal form number that ends with a sequence which repeats indefinitely is rational.

For example, both
`0.3750000[0...]`
and
`6.7292929[29...]` (with the `29` pattern repeating forever)
are rational

An irrational number might look like:
`4.37337333733337...` where the number of `3`'s between `7`'s increases by `1` with each segment of the series
(Note this is only an example. There are many different ways in which the sequence can be non-repeating).