• Math

  Rational or Irrational Numbers

  Posted by Bharti Kumari on January 27, 2024 at 5:30 pm

  How can we identify if a number is rational or irrational?

  Prateek replied 8 months ago 2 Members · 1 Reply

  • mathematics-2
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  Prateek

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  January 31, 2024 at 5:32 pm

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

  1. 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.

  2. 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.

  3. 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.

  4. Determine if the decimal representation repeats:

     • If the decimal representation of the number is non-terminating but repeats a pattern, then it is rational.
     • For example, 0.333…, 0.123123123…, and -0.666… are all rational numbers.

  5. 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, √2, π (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.

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