Question

\( 3.\overline{783} \) $=$ ?

• A. \( 3 \frac{21}{29} \)
• B. \( 3 \frac{23}{29} \)
• C. \( 3 \frac{29}{37} \)
• D. \( 3 \frac{31}{37} \)

Hint:

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.

Answer 1

The Correct Option is C

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.