what do you do to check whether a number is rational or irrational? In your explanation, use an example of irrational and rational number.
To check whether a number is rational or irrational, you need to examine its decimal representation and determine if it terminates or repeats, or if it goes on indefinitely without repeating. Here's how you can do that:
1. Rational Numbers:
Rational numbers can be expressed as a fraction, where both the numerator and the denominator are integers. To check if a number is rational, you need to convert it into a fraction or determine if its decimal representation terminates or repeats.
Example of a rational number: 0.75
To convert 0.75 into a fraction, you can write it as 75/100. Since both the numerator and the denominator are integers, 0.75 is a rational number.
2. Irrational Numbers:
Irrational numbers cannot be expressed as a fraction of two integers, and their decimal representation goes on indefinitely without repeating. To check if a number is irrational, you need to examine its decimal representation for any patterns or repeating digits.
Example of an irrational number: √2 (square root of 2)
The decimal representation of √2 is approximately 1.41421356... It goes on indefinitely without repeating or terminating, and no pattern can be observed. Hence, √2 is an irrational number.
By analyzing the decimal representation and looking for patterns or repetition, you can determine whether a number is rational or irrational.