Is -10 a rational number or irrational? This question may seem simple at first glance, but it touches upon the fascinating world of mathematics and the classification of numbers. In this article, we will explore the definition of rational and irrational numbers, and determine whether -10 falls into one of these categories.
Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. They can be further divided into two types: integers and fractions. Integers are whole numbers, such as 1, -1, 2, -2, and so on. Fractions, on the other hand, are numbers that represent parts of a whole, like 1/2, 3/4, -2/3, and so on.
Irrational numbers, in contrast, cannot be expressed as a fraction of two integers. They are non-terminating and non-repeating decimals, such as π (pi), √2 (square root of 2), and e (Euler’s number). These numbers have decimal expansions that continue indefinitely without repeating patterns.
Now, let’s analyze the number -10. It is a negative integer, which means it is a whole number less than zero. Integers are a subset of rational numbers, as they can be expressed as fractions with a denominator of 1. Therefore, -10 can be written as -10/1, which is a fraction of two integers.
Since -10 can be expressed as a fraction of two integers, it falls into the category of rational numbers. This conclusion is consistent with the definition of rational numbers, which states that they can be represented as a fraction of two integers.
In conclusion, -10 is a rational number, not an irrational one. This determination highlights the importance of understanding the properties of different types of numbers in mathematics, as it allows us to classify and analyze them effectively.
