Is 8 an irrational number? This question may seem paradoxical at first glance, as 8 is a whole number and is typically associated with rational numbers. However, the nature of 8 as a rational or irrational number can be explored through the definitions and properties of these two types of numbers.
Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. This means that rational numbers can be written in the form of p/q, where p and q are integers and q is not equal to zero. On the other hand, irrational numbers cannot be expressed as a fraction of two integers and have decimal expansions that are non-terminating and non-repeating.
At first glance, 8 seems to fit the definition of a rational number, as it can be written as 8/1, where both 8 and 1 are integers. However, this does not necessarily mean that 8 is an irrational number. To determine whether 8 is irrational, we need to consider the properties of its decimal expansion.
The decimal expansion of 8 is simply 8.0, which is a terminating decimal. This means that the decimal expansion of 8 ends after a finite number of digits, and it does not continue indefinitely. Since the decimal expansion of 8 is terminating, it can be expressed as a fraction of two integers, making 8 a rational number.
In conclusion, the question “Is 8 an irrational number?” can be answered with a definitive “no.” 8 is a rational number because it can be expressed as a fraction of two integers, and its decimal expansion is terminating. This example highlights the importance of carefully examining the properties of numbers when determining their classification as rational or irrational.
