Question
The simplest form of \(1.\overline{6}\) is:
(a) \( \frac{8}{5} \)
(b) \( \frac{5}{3} \)
(c) \( \frac{833}{500} \)
(d) \( \frac{7}{6} \)
Solution
Let \( x = 1.\overline{6} \)
\[ x = 1.6666\ldots \]
Multiply both sides by 10:
\[ 10x = 16.6666\ldots \]
Subtract the first equation from the second:
\[ 10x – x = 16.6666\ldots – 1.6666\ldots \]
\[ 9x = 15 \]
\[ x = \frac{15}{9} = \frac{5}{3} \]
Final Answer
✔ Correct option: (b) \( \frac{5}{3} \)