Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{400}{11}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{6}&\phantom{.}&\phantom{3}&\phantom{6}&\phantom{3}&\phantom{6}\end{array}&\\11&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $11$'s are in $4$? The answer is $0$.

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

Now, $4-0 \cdot 11 = 4 - 0= 4$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{DarkBlue}{0}&\phantom{3}&\phantom{6}&\phantom{.}&\phantom{3}&\phantom{6}&\phantom{3}&\phantom{6}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{DarkBlue}{4}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $11$'s are in $40$? The answer is $3$.

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

Now, $40-3 \cdot 11 = 40 - 33= 7$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{OrangeRed}{3}&\phantom{6}&\phantom{.}&\phantom{3}&\phantom{6}&\phantom{3}&\phantom{6}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}4&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{4}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&3&\phantom{.}\\\hline\phantom{lll}&7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $11$'s are in $70$? The answer is $6$.

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

Now, $70-6 \cdot 11 = 70 - 66= 4$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&3&\color{Chocolate}{6}&\phantom{.}&\phantom{3}&\phantom{6}&\phantom{3}&\phantom{6}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}4&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&3&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{7}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $11$'s are in $40$? The answer is $3$.

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

Now, $40-3 \cdot 11 = 40 - 33= 7$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&3&6&.&\color{BlueViolet}{3}&\phantom{6}&\phantom{3}&\phantom{6}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}4&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&3&\phantom{.}\\\hline\phantom{lll}&7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&6&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{4}&\phantom{.}&\color{BlueViolet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $11$'s are in $70$? The answer is $6$.

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

Now, $70-6 \cdot 11 = 70 - 66= 4$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&3&6&.&3&\color{Crimson}{6}&\phantom{3}&\phantom{6}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}4&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&3&\phantom{.}\\\hline\phantom{lll}&7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&3\\\hline\phantom{lll}&&&&\color{Crimson}{7}&\color{Crimson}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&6&6\\\hline\phantom{lll}&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $11$'s are in $40$? The answer is $3$.

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

Now, $40-3 \cdot 11 = 40 - 33= 7$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&3&6&.&3&6&\color{Peru}{3}&\phantom{6}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}4&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&3&\phantom{.}\\\hline\phantom{lll}&7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&6&6\\\hline\phantom{lll}&&&&&\color{Peru}{4}&\color{Peru}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&3\\\hline\phantom{lll}&&&&&&7&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 7

How many $11$'s are in $70$? The answer is $6$.

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

Now, $70-6 \cdot 11 = 70 - 66= 4$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&3&6&.&3&6&3&\color{DarkMagenta}{6}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}4&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&3&\phantom{.}\\\hline\phantom{lll}&7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&6&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&6&6\\\hline\phantom{lll}&&&&&4&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&3\\\hline\phantom{lll}&&&&&&\color{DarkMagenta}{7}&\color{DarkMagenta}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&6&6\\\hline\phantom{lll}&&&&&&&4\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{400}{11}=36. \overline{36}$

Answer: $\frac{400}{11}=36.\overline{36}$