Is 10 a rational number or irrational? This question may seem simple at first glance, but it touches upon a fundamental concept in mathematics. In order to answer this question, we need to delve into the definitions of rational and irrational numbers.
Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. This means that any number that can be written in the form of p/q, where p and q are integers and q is not equal to zero, is considered rational. On the other hand, irrational numbers are numbers that cannot be expressed as a fraction of two integers. These numbers have decimal expansions that neither terminate nor repeat indefinitely.
Now, let’s analyze the number 10. It can be written as 10/1, where both 10 and 1 are integers and 1 is not equal to zero. Therefore, 10 is a rational number. This is a straightforward example of a rational number, as it can be easily expressed as a fraction.
In contrast, irrational numbers are more complex. They cannot be expressed as fractions of two integers. For instance, the number π (pi) is an irrational number. It is a non-terminating, non-repeating decimal, and it cannot be written as a fraction. Similarly, the square root of 2 (√2) is also an irrational number. It has a decimal expansion that neither terminates nor repeats, making it impossible to express it as a fraction.
To summarize, 10 is a rational number because it can be expressed as a fraction of two integers (10/1). In contrast, irrational numbers like π and √2 cannot be expressed as fractions of two integers and have non-terminating, non-repeating decimal expansions. Understanding the distinction between rational and irrational numbers is crucial in mathematics, as it helps us categorize and analyze numbers in various mathematical contexts.
