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Example 6 - 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 6 Convert 0.(45) ̅ into the form 𝑝/𝑞. Let x = 0.454545… Since two digits repeats (there is bar over 4 & 5) Multiplying equation (1) by 102 i.e. 100 100x = 100 × (0.4545…) 100x = 45.4545… Doing (2) – (1) 100x – x = 45.4545… – 0.4545… Since both have same digits after decimal, we can cancel them 99x = 45 – 0 99x = 45 x = 45/99 x = 15/33 x = 𝟓/𝟏𝟏 Thus, 𝟎.(𝟒𝟓) ̅ = 𝟓/𝟏𝟏
