You are here
Example 5 - Chapter 3 Class 9 - The World of Numbers (Ganita Manjari I)
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
Example 5 Convert 0.6 ̅ into the form 𝑝/𝑞. Let x = 0.666… Since only one digit repeats (there is bar over 6 only) Multiplying equation (1) by 101 i.e. 10 10x = 10 × (0.666…) 10x = 6.666… Doing (2) – (1) 10x – x = 6.666… – 0.666… Since both have same digits after decimal, we can cancel them 9x = 6 – 0 9x = 6 x = 6/9 x = 𝟐/𝟑 Thus, 𝟎.𝟔 ̅ = 𝟐/𝟑
