Beginning Algebra With Applications, Chapter 1, 1.3, Section 1.3, Problem 194

Use a calculator to determine the decimal representations of $\displaystyle \frac{17}{99}, \frac{45}{99}$, and $\displaystyle \frac{73}{99}$. Make a conjecture as to the decimal representation of $\displaystyle \frac{83}{99}$. Does your conjecture work for $\displaystyle \frac{33}{99}$? What about $\displaystyle \frac{1}{99}$?

Using a calculator,


$
\begin{equation}
\begin{aligned}

\frac{17}{99} =& 0.171717...
\\
\\
\frac{45}{99} =& 0.454545...
\\
\\
\frac{73}{99} =& 0.737373...

\end{aligned}
\end{equation}
$


This means that if the denominator is $99$, then the fraction $\displaystyle \frac{83}{99}$ converts into a decimal, the result will be a repeating number of the product of the numerator times $0.01$. So $\displaystyle \frac{83}{99} = 0.8383$. If the fraction is $\displaystyle \frac{33}{99}$ , the result is $0.333333$.... and if the fraction is $\displaystyle \frac{1}{99}$, the result is $0.010101$...