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Ex 3.5, 2
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 ΕhΕ«nya
- 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 βn on Number line
- The Story of Pi (Ο) and Madhavaβs 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, 2 Perform the long division for 1/13. Identify the repeating block of digits. Does it show cyclic properties if you evaluate 2/13? Now compute 3/13, 4/13, etc. What do you notice? Letβs divide π/ππ We notice that 1/13 = 0.(ππππππ) Μ Thus, repeating block of digits is 076923 Evaluating other numerators Let's calculate the next few fractions to see what happens: 2/13=0.(153846) Μ 3/13=0.(230769) Μ 4/13=0.307692 5/13=0.384615 What do you notice? Unlike 1/7, which uses the exact same cyclic block for every single numerator, 13 breaks its fractions into two different cyclic families: The 076923 family: Shared by 1/13, 3/13, 4/13, 9/13, 10/13, and 12/13 (e.g., 3/13 starts at the '2β, 4/13 starts at the '3'). The ππππππ family: Shared by π/ππ,π/ππ,π/ππ,π/ππ,π/ππ
