Question

When 0.232323.... is converted into a fraction, then it is equal to:
1. \(\frac{23}{90}\)
2. \(\frac{23}{100}\)
3. \(\frac{23}{99}\)
4. None of the above

Answer 1

Correct Answer - Option 3 : \(\frac{23}{99}\)

Calculation:

Let assume that 0.232323...... = x  ............   (1)

Multiplying both the sides by 100

0.232323...... × 100 = x × 100

⇒ 23.2323...... = 100 x                   ...............    (2)

Subtraction equation (2) - equation (1)

⇒ 23 = 99x

⇒ x = 23/99 

∴ 0.232323.... = 23/99

The correct option is 3 i.e. 23/99