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Convert 0.363636...... into a fraction.

This question was previously asked in
RPF Constable 2024 Official Paper (Held On 03 Mar, 2025 Shift 2)
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  1. 36/99
  2. 63/99
  3. 3636/1000
  4. 36/100

Answer (Detailed Solution Below)

Option 1 : 36/99
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Detailed Solution

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Given:

Decimal to convert = 0.363636 (repeating).

Calculation:

Let x = 0.363636...

⇒ 100x = 36.363636... (Multiplying by 100 to shift the repeating part)

⇒ 100x - x = 36.363636... - 0.363636...

⇒ 99x = 36

⇒ x = \(\frac{36}{99}\)

The correct fraction is \(\frac{36}{99}\).

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