Question
Download Solution PDFThe conversion of \(0.0 \overline{37}\) in the fractional form is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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