Is -9 a rational number or irrational? This question may seem straightforward, but it raises an interesting discussion about the nature of numbers. To understand whether -9 is a rational number or an irrational number, we need to delve into the definitions of these two types of numbers and analyze the properties of -9 in light of these definitions.
Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. They can be positive, negative, or zero. On the other hand, irrational numbers are real numbers that cannot be expressed as a fraction of two integers. They are non-terminating and non-repeating decimals.
In the case of -9, we can express it as a fraction by writing it as -9/1. Since -9 and 1 are both integers and the denominator is not zero, -9 is a rational number. This means that -9 can be written as a fraction in the form of p/q, where p and q are integers.
Now, let’s consider the properties of -9. It is a negative number, which means that it has a negative sign in front of it. However, the negative sign does not affect the rationality of a number. For example, 9 is a rational number, and -9 is simply the negative of 9. The fact that -9 is negative does not make it irrational.
Moreover, -9 is a whole number, which is a subset of the integers. Whole numbers are also rational numbers because they can be expressed as a fraction with a denominator of 1. Therefore, -9 can be written as -9/1, which is a fraction of two integers.
In conclusion, -9 is a rational number because it can be expressed as a fraction of two integers, -9/1. The negative sign and the fact that it is a whole number do not change its rationality. This discussion highlights the importance of understanding the definitions of rational and irrational numbers to determine the nature of a given number.
