Decimal expansion of real numbers

Last updated at August 8, 2026 by

Decimal expansion of real numbers - Finding decimal expansion

Decimal expansion of real numbers - Part 2

 

 

There are generally 3 types of decimal expansion

  1. Terminating
  2. Non-terminating Repeating
  3. Non-terminating Non Repeating

 

Let us take an example to study it

Decimal expansion of real numbers - Part 3

In 20/8 = 2.5 ,

  • the remainder is 0
  • the decimal ends at 5.

So, that means the expansion is terminating.

 

In 10/3 = 3.3333 …,

  • the expansion does not end i.e. non-terminating
  • and 3 keeps on repeating

So, it is a non-terminating, repeating expansion

 

There are also some decimals like

1.4142135623…

  • the expansion does not end i.e. non-terminating
  • and no set of numbers repeat

So, it is a non-terminating, non-repeating expansion

 

Let us learn how to find decimal expansions of numbers.

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Transcript

Finding Irrational Number b/w two numbers Decimal Expansion Irrational or Rational Practice Questions Decimal Expansion Let’s divide two numbers 20/8 = 2.5 Terminating Decimal Expansion 10/3 = 3.333.. Non-Terminating Repeating Decimal Expansion

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