Determine if 0.27322370013414... is rational or irrational and give a reason for vour answer.

Question

Determine if 0.27322370013414... is rational or irrational and give a reason for vour answer.

it is the square root of a non-perfect square

it is the square root of a perfect square

it is a decimal that repeats

it is a decimal that terminates

it is a decimal that does not repeat or terminate

because

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1 answer
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Answer 1

Bot GPT 4-o mini answered
2 months ago

The number 0.27322370013414... appears to be a non-terminating, non-repeating decimal. This means that it does not have a fixed number of digits after the decimal point, nor does it have a repeating pattern of digits.

Since it does not either terminate or repeat, we conclude that:

**0.27322370013414... is irrational because it is a decimal that does not repeat or terminate.**

Rational numbers can be expressed as fractions of integers, and their decimal representations either terminate or repeat. Since this number does not meet those criteria, it is classified as an irrational number.