Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{100}{36}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\36&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$36$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-36 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{DarkMagenta}{0}&\phantom{0}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{DarkMagenta}{1}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$36$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-36 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{OrangeRed}{0}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{1}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$36$$$'s are in $$$100$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$100-36 \cdot 2 = 100 - 72= 28$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{DarkCyan}{2}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{1}&\color{DarkCyan}{0}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&2&8&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$36$$$'s are in $$$280$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$280-36 \cdot 7 = 280 - 252= 28$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&.&\color{GoldenRod}{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&\color{GoldenRod}{2}&\color{GoldenRod}{8}&\phantom{.}&\color{GoldenRod}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&5&\phantom{.}&2\\\hline\phantom{lll}&&2&\phantom{.}&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$36$$$'s are in $$$280$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$280-36 \cdot 7 = 280 - 252= 28$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&.&7&\color{Violet}{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&2&8&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&5&\phantom{.}&2\\\hline\phantom{lll}&&\color{Violet}{2}&\phantom{.}&\color{Violet}{8}&\color{Violet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&5&2\\\hline\phantom{lll}&&&&2&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$36$$$'s are in $$$280$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$280-36 \cdot 7 = 280 - 252= 28$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&.&7&7&\color{Green}{7}&\phantom{7}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&2&8&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&5&\phantom{.}&2\\\hline\phantom{lll}&&2&\phantom{.}&8&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&5&2\\\hline\phantom{lll}&&&&\color{Green}{2}&\color{Green}{8}&\color{Green}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&5&2\\\hline\phantom{lll}&&&&&2&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$36$$$'s are in $$$280$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$280-36 \cdot 7 = 280 - 252= 28$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&2&.&7&7&7&\color{Brown}{7}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&2&8&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&5&\phantom{.}&2\\\hline\phantom{lll}&&2&\phantom{.}&8&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&5&2\\\hline\phantom{lll}&&&&2&8&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&5&2\\\hline\phantom{lll}&&&&&\color{Brown}{2}&\color{Brown}{8}&\color{Brown}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&5&2\\\hline\phantom{lll}&&&&&&2&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{100}{36}=2.77 \overline{7}$$$

Answer: $$$\frac{100}{36}=2.77\overline{7}$$$