Determine if 0.828228222822228222228... is rational or irrational and give a reason for your answer.

Question

it is a decimal that repeats

it is the square root of a non-perfect square

it is a decimal that does not repeat or terminate

it is a decimal that terminates

it is the square root of a perfect square

ational

because

V

Answer 1

The decimal \(0.828228222822228222228...\) is a repeating decimal because the sequence "2228" repeats indefinitely.

A number is considered rational if it can be expressed as a fraction \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\). Since \(0.828228222822228222228...\) has a repeating part, it can be expressed as a fraction.

Consequently, the correct classification for \(0.828228222822228222228...\) is:

It is rational.

Reason: Because it is a decimal that repeats.