Rewrite as a simplified fraction.
\[\large{3.1\overline{6} = ?}\]
1 answer
To rewrite the decimal number $3.1\overline{6}$ as a simplified fraction, we will let $x=3.1\overline{6}$. Multiplying both sides of this equation by a power of $10$ allows us to shift the decimal point to get rid of the repeating part. Since there is only one digit repeated, multiplying by $10$ is sufficient. We find $$10x=31.\overline{6}.$$ Notice how subtracting the original equation from this new equation eliminates the repeating part and leaves us with only $10x-x=31.\overline{6}-3.1\overline{6}=28$. Solving $10x-x=28$ for $x$ shows that $x=\boxed{\frac{28}{9}}.$
1 answer