Is 0.571428 a rational or irrational number?

2 Answers
Apr 3, 2018

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.

Apr 3, 2018

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