Бројеви у децималном запису

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Пр.1)   Дате периодичне децималне бројеве написати у облику

           разломака:

           а) 0,1111...    б) 2,4545...   в) -0,16666...   г) -1,888...

           д) 2,416666...   ђ) -3,5333...

Пр.1)   

\[\begin{array}{*{20}{c}}
{x = 0,111...}&{}&{x = 2,4545...}&{}&{} \\
{10x = 1,11...}&{}&{100x = 245,4...}&{}&{} \\
{10x - x = 1,111... - 0,111...}&{}&{100x - x = 245,4... - 2,4545...}&{}&{} \\
{9x = 1}&{}&{99x = 243}&{}&{} \\
{x = \frac{1}{9}}&{}&{x = \frac{{243}}{{99}} = \frac{{27}}{{11}} = 2\frac{5}{{11}}}&{}&{} \\
{}&{}&{}&{}&{} \\
{}&{}&{}&{}&{} \\
{}&{}&{}&{}&{}
\end{array}\]

\[\begin{array}{*{20}{c}}
\begin{gathered}
x = - 0,1666... \hfill \\
10x = - 1,66... \hfill \\
10x - x = - 1,66... + 0,166... \hfill \\
9x = - 1,5 \hfill \\
x = - \frac{{1,5}}{9} \hfill \\
x = - \frac{3}{{18}} \hfill \\
x = - \frac{1}{6} \hfill \\
\end{gathered} &{}&{}&\begin{gathered}
x = - 1,888... \hfill \\
10x = - 18,888... \hfill \\
10x - x = - 18,888... + 1,888... \hfill \\
9x = - 17 \hfill \\
x = - \frac{{17}}{9} \hfill \\
x = - 1\frac{8}{9} \hfill \\
\hfill \\
\end{gathered}
\end{array}\]

\[\begin{array}{*{20}{c}}
\begin{gathered}
x = 2,41666... \hfill \\
10x = 24,166... \hfill \\
10x - x = 24,166... - 2,4166... \hfill \\
9x = 21,75 \hfill \\
x = \frac{{21,75}}{9} \hfill \\
x = \frac{{87}}{{36}} \hfill \\
x = \frac{{29}}{{12}} \hfill \\
x = 2\frac{5}{{12}} \hfill \\
\end{gathered} &{}&{}&\begin{gathered}
x = - 3,5333... \hfill \\
10x = - 35,333... \hfill \\
10x - x = - 35,333... + 3,533... \hfill \\
9x = - 31,8 \hfill \\
x = - \frac{{31,8}}{9} \hfill \\
x = - \frac{{159}}{{45}} \hfill \\
x = - \frac{{53}}{{15}} \hfill \\
x = - 3\frac{8}{{15}} \hfill \\
\end{gathered}
\end{array}\]