Only for rational numbers. Decimal -> fraction is a surjection. Irractional numbers, notionally representable as decimals, are uncountably infinite, and do not map 1:1 to fractions.
It is literally a ratio of integers, therefore rational.
Correct, rational numbers are those numbers that can be represented as a ratio of integers (excluding zero as denominator). Our points agree.
It is rational: 391/1250
(Note: this was a mistyping of 381/1250)
This particular value is, certainly.
I think you’re technically equating non terminating to irrational but the looser point seems fair to me— it’s hard to codify precise decimals.
Close. Many non-terminating can be mapped to fractions (e.g. 0.88888... = 8/9), which is equivalent to rational, but non-terminating and non-repeating are irrational (e.g. π or e).
I guess I’m just making the point all nonterninating are hard to codify in non mathematical fonts formatting etc. For instance using that 0.88888 example, that decimal very much does not precisely equal 8/9. you’d either have to keep writing 8s into infinity or hope everybody who copies/Padres your writing has a way to preserve the indicator of repeating digits.