Identifying Rational Numbers- Which of the Following is a Rational Number-_1

Which of the following is a rational number? This question often arises in mathematics, especially when dealing with real numbers. A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero. In this article, we will explore some examples and properties of rational numbers to help you identify them among other numbers.

Rational numbers are an essential part of the number system, as they encompass all numbers that can be written as a ratio of two integers. They are widely used in various fields, such as science, engineering, and finance. To understand rational numbers better, let’s take a closer look at some examples.

One of the simplest rational numbers is 3, which can be written as the fraction 3/1. Similarly, 0.5 is a rational number, as it can be expressed as 1/2. These examples show that rational numbers can be positive, negative, or zero.

Another example of a rational number is -2, which can be written as -2/1. Rational numbers can also be fractions with different denominators, such as 1/3, 5/7, or 8/9. As long as these fractions can be simplified to a ratio of two integers, they are considered rational numbers.

It is important to note that not all numbers are rational. For instance, the square root of 2 (√2) is an irrational number, as it cannot be expressed as a fraction of two integers. Irrational numbers are those that cannot be written as a ratio of two integers and often have decimal expansions that do not terminate or repeat.

To determine whether a number is rational or irrational, you can use the following methods:

1. If a number is a fraction with a non-zero denominator, it is rational.
2. If a number has a terminating decimal expansion, it is rational.
3. If a number has a repeating decimal expansion, it is rational.
4. If a number has a non-terminating, non-repeating decimal expansion, it is irrational.

Now that we have discussed the properties of rational numbers, let’s examine some of the famous irrational numbers, such as π (pi) and e (Euler’s number). While these numbers are not rational, they are still important in various mathematical and scientific applications.

In conclusion, rational numbers are an integral part of the number system, as they can be expressed as a fraction of two integers. By understanding the properties of rational numbers and distinguishing them from irrational numbers, you can gain a better grasp of the fascinating world of mathematics. So, the next time you encounter the question “which of the following is a rational number?” you will be well-equipped to identify the correct answer.