Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{1300}{18}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{2}&\phantom{.}&\phantom{2}&\phantom{2}&\phantom{2}\end{array}&\\18&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&3&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$18$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-18 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Red}{0}&\phantom{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{2}&\phantom{2}&\phantom{2}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Red}{1}& 3 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$18$$$'s are in $$$13$$$?

The answer is $$$0$$$.

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

Now, $$$13-18 \cdot 0 = 13 - 0= 13$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Blue}{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{2}&\phantom{2}&\phantom{2}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&3& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{1}&\color{Blue}{3}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$18$$$'s are in $$$130$$$?

The answer is $$$7$$$.

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

Now, $$$130-18 \cdot 7 = 130 - 126= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{DeepPink}{7}&\phantom{2}&\phantom{.}&\phantom{2}&\phantom{2}&\phantom{2}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&3&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{1}&\color{DeepPink}{3}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$18$$$'s are in $$$40$$$?

The answer is $$$2$$$.

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

Now, $$$40-18 \cdot 2 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&\color{Crimson}{2}&\phantom{.}&\phantom{2}&\phantom{2}&\phantom{2}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&3&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&&\color{Crimson}{4}&\color{Crimson}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$18$$$'s are in $$$40$$$?

The answer is $$$2$$$.

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

Now, $$$40-18 \cdot 2 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&2&.&\color{Violet}{2}&\phantom{2}&\phantom{2}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&3&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&6&\phantom{.}\\\hline\phantom{lll}&&&\color{Violet}{4}&\phantom{.}&\color{Violet}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$18$$$'s are in $$$40$$$?

The answer is $$$2$$$.

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

Now, $$$40-18 \cdot 2 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&2&.&2&\color{DarkCyan}{2}&\phantom{2}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&3&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&&\color{DarkCyan}{4}&\color{DarkCyan}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&6\\\hline\phantom{lll}&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$18$$$'s are in $$$40$$$?

The answer is $$$2$$$.

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

Now, $$$40-18 \cdot 2 = 40 - 36= 4$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&2&.&2&2&\color{DarkMagenta}{2}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&3&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&&4&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&6\\\hline\phantom{lll}&&&&&&\color{DarkMagenta}{4}&\color{DarkMagenta}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&3&6\\\hline\phantom{lll}&&&&&&&4\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1300}{18}=72.2 \overline{2}$$$

Answer: $$$\frac{1300}{18}=72.2\overline{2}$$$