Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{900}{11}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{8}&\phantom{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\11&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$11$$$'s are in $$$9$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$9-11 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{SaddleBrown}{0}&\phantom{8}&\phantom{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{SaddleBrown}{9}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$11$$$'s are in $$$90$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$90-11 \cdot 8 = 90 - 88= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{GoldenRod}{8}&\phantom{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}9&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{9}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$11$$$'s are in $$$20$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$20-11 \cdot 1 = 20 - 11= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&8&\color{Green}{1}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}9&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&\color{Green}{2}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$11$$$'s are in $$$90$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$90-11 \cdot 8 = 90 - 88= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&8&1&.&\color{BlueViolet}{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}9&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&1&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{9}&\phantom{.}&\color{BlueViolet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$11$$$'s are in $$$20$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$20-11 \cdot 1 = 20 - 11= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&8&1&.&8&\color{DarkMagenta}{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}9&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&8\\\hline\phantom{lll}&&&&\color{DarkMagenta}{2}&\color{DarkMagenta}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&1\\\hline\phantom{lll}&&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$11$$$'s are in $$$90$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$90-11 \cdot 8 = 90 - 88= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&8&1&.&8&1&\color{Brown}{8}&\phantom{1}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}9&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&1\\\hline\phantom{lll}&&&&&\color{Brown}{9}&\color{Brown}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&8\\\hline\phantom{lll}&&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$11$$$'s are in $$$20$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$20-11 \cdot 1 = 20 - 11= 9$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&8&1&.&8&1&8&\color{DarkCyan}{1}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}9&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&1\\\hline\phantom{lll}&&&&&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&8\\\hline\phantom{lll}&&&&&&\color{DarkCyan}{2}&\color{DarkCyan}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&1\\\hline\phantom{lll}&&&&&&&9\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{900}{11}=81. \overline{81}$$$

Answer: $$$\frac{900}{11}=81.\overline{81}$$$