Question:
\( 3.\overline{783} \) $=$ ?
\( 3.\overline{783} \) $=$ ?
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To convert a repeating decimal into a fraction, multiply by a power of 10 to shift the decimal point, then subtract the original equation to eliminate the repeating part.
Updated On: Mar 20, 2026
- \( 3 \frac{21}{29} \)
- \( 3 \frac{23}{29} \)
- \( 3 \frac{29}{37} \)
- \( 3 \frac{31}{37} \)
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The Correct Option is C
Solution and Explanation
Define \(x = 3.\overline{783}\) and calculate as follows:
\begin{align}
1000x &= 3783.\overline{783},
1000x - x &= 3783.\overline{783} - 3.\overline{783},
999x &= 3780,
x &= \frac{3780}{999} = \frac{140}{37}. \end{align} Convert \(\frac{140}{37}\) to a mixed number: \[ x = 3\frac{29}{37}. \] This value matches Option 3.
1000x - x &= 3783.\overline{783} - 3.\overline{783},
999x &= 3780,
x &= \frac{3780}{999} = \frac{140}{37}. \end{align} Convert \(\frac{140}{37}\) to a mixed number: \[ x = 3\frac{29}{37}. \] This value matches Option 3.
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