How to check if a number is irrational or rational
To check if a number is irrational or rational, you can follow these steps:
Step 1: Determine if the number is a decimal.
- If it is a decimal, continue to step 2.
- If it is not a decimal (e.g., a fraction or whole number), then it is automatically rational.
Step 2: Write the number in decimal form (if not already).
- If the number is already in decimal form, go to step 3.
- If the number is a fraction or whole number, convert it to decimal form by performing the division.
Step 3: Analyze the decimal representation of the number.
- If the decimal representation terminates (i.e., ends after a finite number of decimal places), then the number is rational.
- If the decimal representation repeats indefinitely (i.e., has a repeating pattern of one or more digits after some point), then the number is rational.
- If the decimal representation does not terminate or repeat (i.e., keeps going without any pattern), then the number is irrational.
Note: It is impossible to determine with 100% certainty if a number is irrational, as the decimal representation might exhibit a pattern that is not immediately obvious. However, using this method, you can identify many rational numbers and determine if a number is likely to be irrational.