Simplest Form of \(1.\overline{6}\)
Fill in the Blank:
The simplest form of \(1.\overline{6}\) is \(\frac{5}{3}\).
Explanation:
Let \(x = 1.666\ldots\)
\[ 10x = 16.666\ldots \]
\[ 10x – x = 16.666\ldots – 1.666\ldots \]
\[ 9x = 15 \Rightarrow x = \frac{15}{9} = \frac{5}{3} \]
Final Answer:
\(\frac{5}{3}\)