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Decimal Expansion of Real Numbers
Last updated at May 11, 2026 by Teachoo
Decimal Expansion of Real Numbers
Class 9
Chapter 3 Class 9 - The World of Numbers (Ganita Manjari I)
- The Human Need to Count
- Exercise Set 3.1
- The Revolution of Śhūnya
- Integers
- Exercise Set 3.2
- Rational Numbers
- Exercise Set 3.3
- Rational Numbers on the Number Line
- Absolute Value of a Rational Number
- Rational Numbers between two Rational numbers
- Exercise Set 3.4
- Irrational Numbers
- Construction of Length √n on Number line
- The Story of Pi (π) and Madhava’s Infinite Series
- Real Numbers & Imaginary Numbers
-
Decimal Expansion of Real Numbers
- Magic of Cyclic Numbers
- Constructing a Square Root Spiral
- Exercise Set 3.5
- End-of-Chapter Exercises
Transcript
Decimal Expansion of Real Numbers Decimal Expansion Terminating Non-Terminating Example: 2.5, 3.2, 9.99 Rational Non-Terminating Repeating Example: 3.333…, 2.1911111… Rational Non-Terminating Non-Repeating Example: 1.41421356237…, 3.14159265359… Irrational Let’s do some examples Divinding 𝟐𝟎/𝟖 Thus, 𝟐𝟎/𝟖=𝟐.𝟓 Dividing 𝟏𝟎/𝟑 Thus, 𝟏𝟎/𝟑=𝟑.𝟑𝟑𝟑… Terminating Decimal Expansion Rational Non-Terminating Repeating Decimal Expansion Rational Are all Decimal Expansions Fractions? No. What about 𝝅 or √𝟐? 𝝅 = 3.1415926535897932384626433832795… √𝟐 = 1.4142135623730950488…. These are non-terminating, non repeating decimal expansion Hence, There are 3 types of Decimal Expansion Terminating Non-Terminating Repeating Non-Terminating Non-Repeating Can be written in fraction So, Rational Number Cannot be written in fraction So, Irrational Number
