Question

Is 0.571428 a rational or irrational number?

Answer 1

It is a rational number.

Explanation:

It is a rational number. Bcoz it is terminating & non-recurring.
`0.571428=571428/10^6`, where `10^6cancel=0`, which is the equation of rational numbers.

Answer 2

Rational, whether you meant `0.571428` or `0.bar(571428)`

Explanation:

Any terminating or repeating decimal is rational.

If by `0.571428` you actually meant the `6` digit terminating decimal then it is equal to:

`571428/1000000 = (color(red)(cancel(color(black)(4))) * 142857)/(color(red)(cancel(color(black)(4))) * 250000) = 142857/250000`

If by `0.571428` you really meant the recurring decimal:

`0.bar(571428) = 0.571428571428571428...`

then note that:

`(1000000-1)0.bar(571428) = 571428.bar(571428)-0.bar(571428) = 571428`

So:

`0.bar(571428) = 571428/(1000000-1) = 571428/999999 = (color(red)(cancel(color(black)(142857))) * 4)/(color(red)(cancel(color(black)(142857))) * 7) = 4/7`