Question

Find an irrational number between 0.9 and 1​

Answer 1

an irrational no between 0.9 and 1 is 0.9999999999..

Answer 2

Answer:

1/1

Step-by-step explanation:

Maybe you think a repeating decimal is irrational. But it is not. Not if there is a pattern of repetition. Of course for .999…. the pattern is repeating 9’s.

The formal definition of a rational number says you must be able to write it as the quotient of two integers. (or simply as a fraction,)

.999... is NOT irrational because it CAN be written as the ratio of 2 integers, namely 1/1.

It IS a repeating decimal.

I'll show you how .999... = 1.

1/3 + 1/3 + 1/3 = 3/3 = 1. And

.33... + .33... + .33... = .99...

Since 1/3 = .33... then .99... = 1

by the Transitive Property of Equivalence Relations. And 1 = 1/1.