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The numbers 2.8888......and 2.99999...... are both rational numbers. What is an irrational number that is between the two rational numbers?

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Answer:

  √8.7

Step-by-step explanation:

There are an infinite number of irrational numbers between any pair of rational numbers. So, there are an infinite number of possible answers

One such would be ...

  2.898998999899998... where the number of repeated 9s increases by 1 in each instance. This is a never-ending non-repeating decimal, hence irrational.

Another irrational number is ...

  √8.7 ≈ 2.949576240750525... never ending, never repeating

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Additional comment

A repeating single digit is equivalent to the fraction with that digit divided by 9. Hence 2.99999... = 2 9/9 = 3.