Which of the following appears to be an irrational number?

Question

(1 point)
• 3.72727272…
•
• –
• .073303330…

Answer 1

Rational number is a number that can be expressed as fraction p / q
were p and q are two integers.

3.72727272… = 4 / 11

So 3.72727272... is rational number.

0.073303330... is not rational number because:

0.073303330330330... =

7330 / 100000 + 30333 / 10000000000 + 33033/100000000000000 +...=

7330 / 10⁵ + 30333 / 10¹⁰ + 30333 / 10¹⁰ + 30333 / 10¹⁴ +...

We need to divide 30333 by some exponent of 10 an infinite number of times.

So 0.073303330... is irrational number