The conversion of \(0.0 \overline{37}\) in the fractional form is

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Assam ADRE SLRC 2022 Paper IV
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  1. \(\frac{37}{990}\)
  2. \(\frac{37}{999}\)
  3. \(\frac{37}{100}\)
  4. \(\frac{37}{1000}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{37}{990}\)
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Detailed Solution

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Given:

Decimal number = 0.0\(\overline{37}\)

Calculations:

Let x = 0.0\(\overline{37}\)

⇒ x = 0.0373737...

Multiply by 10 to move the non-repeating part past the decimal:

⇒ 10x = 0.373737... (Equation 1)

Multiply by 1000 to move one full cycle of the repeating part past the decimal:

⇒ 1000x = 37.373737... (Equation 2)

Subtract Equation 1 from Equation 2:

⇒ 1000x - 10x = 37.373737... - 0.373737...

⇒ 990x = 37

Solve for x:

⇒ x = \(\frac{37}{990}\)

∴ The fractional form of 0.0\(\overline{37}\) is \(\frac{37}{990}\).

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