In order to determine which of the given numbers are irrational, we need to understand what constitutes an irrational number. An irrational number is a number that cannot be expressed as a simple fraction.
Let's analyze each option:
1) The first number, 8/9, is a fraction of two integers, 8 and 9. Since all fractions are rational numbers, i.e., they can be expressed as a certain ratio of two integers, 8/9 is a rational number, not an irrational one.
2) The second number is π (pi). The value of pi is approximately 3.14159, but it continues indefinitely without repeating and cannot be exactly expressed as a fraction. This fits the definition of an irrational number. Hence, pi is an irrational number.
3) The third number, 2.3 (with the 3 repeating), is a repeating decimal. Repeating decimals, like fractions, are also rational numbers as they can be expressed as a fraction. For instance, 2.3 recurring can be expressed as 23/10, thus categorizing it as a rational number.
4) The last number, 1.5, is another fraction (1+1/2) and thus, it is also a rational number.
So, after analyzing all the given choices, we conclude that only π (pi) is an irrational number.
Answer: 2) π (pi)