Final answer:
The number 58 is a rational number because it can be expressed as the fraction 58/1, with a non-zero denominator. Being an integer, 58 is inherently rational since it can be represented as itself over one, meeting criteria for rational numbers.
Step-by-step explanation:
To determine if 58 is irrational or rational, we should first understand what rational and irrational numbers are. A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero. Conversely, an irrational number is a number that cannot be expressed as a simple fraction; its decimal form goes on forever without repeating.
In the case of 58, it can be expressed as the fraction 58/1, which clearly shows two integers with a non-zero denominator. Thus, 58 is a rational number. Additionally, 58 is a whole number, and all whole numbers are inherently rational because they can be represented as themselves divided by one.
It’s also important to check if the answer is reasonable. In this scenario, ensuring that the number meets the criteria for being rational or irrational is part of assessing its reasonableness. 58 does not possess characteristics of irrational numbers, such as non-repeating, non-terminating decimals or being the result of the square root of a non-perfect square. Using these strategies, we can confidently say that 58 is rational because it is an integer, represents a point on the number line that corresponds to a perfect division, and can be written as a fraction with an integer numerator and denominator.