what do you do to check whether a number is rational or irrational? in your explanation, use an example of an irrational and rational number
To determine whether a number is rational or irrational, we need to first understand what these terms mean. A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. An irrational number, on the other hand, is a number that cannot be expressed as a fraction and has an infinite number of decimals that never repeat.
One way to check whether a number is rational or irrational is to try and express it as a fraction. If the number can be written as a fraction, then it is rational. If it cannot be expressed as a fraction, then it is irrational.
For example, let's take the number 1/3. This is a rational number because it can be written as a fraction with integers for both the numerator and the denominator.
Now let's take the number √2, which is the square root of 2. This number cannot be written as a fraction with integers for the numerator and denominator, so it is irrational.
In summary, to check whether a number is rational or irrational, we need to try and express it as a fraction. If we can do so, then it is rational. If we cannot, then it is irrational.
To determine whether a number is rational or irrational, you can follow these steps:
1. Understand the concept: A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. An irrational number, on the other hand, cannot be expressed as a fraction and has an infinite non-repeating decimal representation.
2. Example of a rational number: Let's take the number 1.5. We can express it as a fraction by writing it as 3/2. Here, both the numerator (3) and the denominator (2) are integers, so 1.5 is a rational number.
3. Example of an irrational number: Consider the square root of 2 (√2). It is impossible to express √2 as a fraction with integers for both the numerator and the denominator. When evaluated, √2 is approximately 1.4142135... and the decimal continues infinitely without any repeating pattern. Therefore, √2 is an irrational number.
4. Method to check: One way to determine whether a number is rational or irrational is by attempting to represent it as a fraction. If you can express it as a fraction with integers for both the numerator and the denominator, then the number is rational. However, if you cannot represent it as a fraction, it is irrational.
In summary, to determine whether a number is rational or irrational, you can try expressing it as a fraction. If it can be represented as a fraction with integers for both the numerator and the denominator, then it is rational. If not, it is irrational.