Fraction representation of the \(0.12\overline{54}\) is-

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Rajasthan 3rd Grade (Maths & Science) Official Paper (Held On: 25 Feb 2023 Shift 2)
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  1. \(\frac{1242}{1653}\)
  2. \(\frac{12545}{100000}\)
  3. \(\frac{69}{555}\)
  4. \(\frac{69}{550}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac{69}{550}\)
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Detailed Solution

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Given:

\(0.12 \overline{54}\)

Calculation:

Let, \(0.12 \overline{54}\) = m

⇒ 100m = 12.\(\overline{54}\)

⇒ 100m - m = 12.54\(\overline{54}\) - \(0.12 \overline{54}\)

⇒ 99m = 12.42

⇒ m = \(\dfrac{1242}{9900}\) 

Taking 18 as a common from the fraction,

m = \(\dfrac{69}{550}\)

∴ Fraction representation of the \(0.12 \overline{54}\) is \(\dfrac{69}{550}\).

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