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Rational or Irrational Numbers
Posted by Bharti on January 27, 2024 at 5:30 pmHow can we identify if a number is rational or irrational?
Nitesh replied 4 weeks, 1 day ago 2 Members · 1 Reply 
1 Reply

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To determine whether a number is rational or irrational, you can follow these steps:

Understand the definitions:
 Rational Number: A rational number is a number that can be expressed as a fraction of two integers (where the denominator is not zero). In decimal form, a rational number either terminates or repeats.
 Irrational Number: An irrational number is a number that cannot be expressed as a fraction of two integers. In decimal form, an irrational number neither terminates nor repeats.

Express the number as a fraction (if possible):
 If you can represent the number as a fraction (i.e., the ratio of two integers), then it is rational.
 For example, 1/2, 3/4, and 5/7 are all rational numbers.

Check the decimal representation:
 If the decimal representation of the number terminates (i.e., it has a finite number of digits after the decimal point), then it is rational.
 For example, 0.25, 3.0, and 1.75 are all rational numbers.

Determine if the decimal representation repeats:
 If the decimal representation of the number is nonterminating but repeats a pattern, then it is rational.
 For example, 0.333…, 0.123123123…, and 0.666… are all rational numbers.

If the decimal representation neither terminates nor repeats, the number is irrational:
 If the decimal representation goes on indefinitely without any repeating pattern, then the number is irrational.
 For example, âˆš2, Ï€ (pi), and e (Euler’s number) are all irrational numbers.
It’s worth noting that some numbers can be tricky to determine without advanced mathematical techniques. If you’re dealing with a complex number or a number that involves mathematical constants, it may require further analysis.
