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Example 7 - 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 7 Convert 0.16 ̅ into the form 𝑝/𝑞. Let x = 0.16666….. Since this is a general repeating decimal, so we look at both non-repeating (after decimal points) and repeating digits Here, ‘1’ is non-repeating (1 digit), ‘6’ repeats (1 digit). Since one digit is non-repeating (i.e. after decimal point) Multiplying equation (1) by 101 i.e. 10 10x = 10 × (0.16666…) 10x = 1.6666… Since one digit is repeating Multiplying equation (2) by 101 i.e. 10 10 × 10x = 10 × (1.6666…) 100x = 16.6666… Doing (2) – (1) 100x – 10x = 16.666… – 1.666… Since both have same digits after decimal, we can cancel them 90x = 16 – 1 90x = 15 x = 15/90 x = 3/18 x = 𝟏/𝟔 Thus, 0.16 ̅ = 𝟏/𝟔
