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![[Class 9] The number 0.9 (which means 0.99999 … ) is a rational number - Exercise Set 3.5](https://cdn.teachoo.com/b3e4beb4-ae8f-4eab-9b46-3239de7ccccc/slide30.jpg)
Ex 3.5, 4
Last updated at May 12, 2026 by Teachoo
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
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Exercise Set 3.5
- End-of-Chapter Exercises
Transcript
Ex 3.5, 4 The number 0.9 ̅ (which means 0.99999 … ) is a rational number. Using algebra (let x = 0.9 ̅, multiply by 10, and subtract), explain why 0.9 ̅ is exactly equal to 1. Let x = 0.999… Since only one digit repeats (there is bar over 9 only) Multiplying equation (1) by 101 i.e. 10 10x = 10 × (0.999…) 10x = 9.999… Doing (2) – (1) 10x – x = 9.999… – 0.999… Since both have same digits after decimal, we can cancel them 9x = 9 – 0 9x = 9 x = 9/9 x = 1 Thus, 𝟎.𝟗 ̅ = 1 So, we proved why 0.9 ̅ = 1
