Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{600}{9}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\9&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}6&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $9$'s are in $6$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $6-0 \cdot 9 = 6 - 0= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Peru}{0}&\phantom{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Peru}{6}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $9$'s are in $60$? The answer is $6$.

Write down the calculated result in the upper part of the table.

Now, $60-6 \cdot 9 = 60 - 54= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DeepPink}{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{6}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $9$'s are in $60$? The answer is $6$.

Write down the calculated result in the upper part of the table.

Now, $60-6 \cdot 9 = 60 - 54= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&6&\color{BlueViolet}{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&\color{BlueViolet}{6}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $9$'s are in $60$? The answer is $6$.

Write down the calculated result in the upper part of the table.

Now, $60-6 \cdot 9 = 60 - 54= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&6&6&.&\color{Violet}{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&4&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{6}&\phantom{.}&\color{Violet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $9$'s are in $60$? The answer is $6$.

Write down the calculated result in the upper part of the table.

Now, $60-6 \cdot 9 = 60 - 54= 6$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&6&6&.&6&\color{SaddleBrown}{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&\phantom{.}&4\\\hline\phantom{lll}&&&&\color{SaddleBrown}{6}&\color{SaddleBrown}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&4\\\hline\phantom{lll}&&&&&6\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{600}{9}=66. \overline{6}$

Answer: $\frac{600}{9}=66.\overline{6}$