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Mathematics

When 8.328.\overline{32} is expressed as a vulgar fraction, then it becomes :

  1. 208824\dfrac{208}{824}

  2. 82499\dfrac{824}{99}

  3. 80099\dfrac{800}{99}

  4. 41645\dfrac{416}{45}

Rational Irrational Nos

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Answer

Let x = 8.328.\overline{32}

⇒ x = 8.32323232..     ……….(1)

Multiplying both sides by 100 (since there are two recurring digits)

⇒ 100x = 832.3232..     ……….(2)

Subtracting equation (1) from (2), we get :

⇒ 100x - x = 832.3232.. - 8.3232..

⇒ 99x = 824

⇒ x = 82499\dfrac{824}{99}

Hence, Option 2 is the correct option.

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