Keyshia said that one of the following numbers is IRRATIONAL. Which number is IRRATIONAL and why is it IRRATIONAL?
(-2/3,2/3,0.666...,or 0.676676667...)
To determine which number is irrational, we need to understand what irrational numbers are. An irrational number is a real number that cannot be expressed as a ratio of two integers (a fraction) and cannot be represented as a terminating or repeating decimal.
Let's examine each option:
1. -2/3: This number is a rational number since it can be expressed as a fraction. Therefore, it is not irrational.
2. 2/3: Similarly, this number is a rational number since it can be represented as a fraction. Therefore, it is not irrational.
3. 0.666...: This decimal represents the repeating decimal form of 2/3. Although it repeats indefinitely, it can be converted to a fraction. Hence, it is a rational number and not irrational.
4. 0.676676667...: This number is irrational because it neither terminates nor repeats. It is a non-repeating decimal that goes on indefinitely without any pattern. As such, it cannot be expressed as a fraction, making it irrational.
Therefore, the answer to the question is 0.676676667..., which is irrational because it cannot be written as a ratio of two integers and does not terminate or repeat.