Decimal expansion of real numbers

Last updated at Dec. 16, 2024 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo