Is -3 a rational or irrational number? This question often arises when discussing the classification of numbers in mathematics. In order to answer this question, we need to understand the definitions of rational and irrational numbers and then analyze the nature of -3 in this context.
Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. They can be either positive or negative. On the other hand, irrational numbers cannot be expressed as a fraction of two integers and have non-terminating, non-repeating decimal expansions.
To determine whether -3 is rational or irrational, we can examine its representation. Since -3 is an integer, it can be written as a fraction by placing it over 1, which is also an integer. Therefore, -3 can be expressed as -3/1, which is a fraction of two integers. This means that -3 is a rational number.
It is important to note that the negative sign does not affect the rationality or irrationality of a number. For example, both 3 and -3 are rational numbers, as they can both be expressed as fractions of two integers. Similarly, both 3 and -3 have terminating decimal expansions (3.0 and -3.0, respectively), which further confirms their rational nature.
In conclusion, -3 is a rational number because it can be expressed as a fraction of two integers, -3/1. This classification holds true regardless of the sign of the number, as both positive and negative integers are considered rational. Understanding the distinction between rational and irrational numbers is crucial in mathematics, as it helps us to categorize and analyze numbers in various mathematical operations and applications.
