Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{500}{18}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\18&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}5&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$18$$$'s are in $$$5$$$?

The answer is $$$0$$$.

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

Now, $$$5-18 \cdot 0 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{OrangeRed}{0}&\phantom{2}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{OrangeRed}{5}& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$18$$$'s are in $$$50$$$?

The answer is $$$2$$$.

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

Now, $$$50-18 \cdot 2 = 50 - 36= 14$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Brown}{2}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{5}&\color{Brown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$18$$$'s are in $$$140$$$?

The answer is $$$7$$$.

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

Now, $$$140-18 \cdot 7 = 140 - 126= 14$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&\color{DeepPink}{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{1}&\color{DeepPink}{4}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&1&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$18$$$'s are in $$$140$$$?

The answer is $$$7$$$.

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

Now, $$$140-18 \cdot 7 = 140 - 126= 14$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&7&.&\color{DarkMagenta}{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&\color{DarkMagenta}{1}&\color{DarkMagenta}{4}&\phantom{.}&\color{DarkMagenta}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&2&\phantom{.}&6\\\hline\phantom{lll}&&1&\phantom{.}&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$18$$$'s are in $$$140$$$?

The answer is $$$7$$$.

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

Now, $$$140-18 \cdot 7 = 140 - 126= 14$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&7&.&7&\color{Chocolate}{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&1&4&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&2&\phantom{.}&6\\\hline\phantom{lll}&&\color{Chocolate}{1}&\phantom{.}&\color{Chocolate}{4}&\color{Chocolate}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&2&6\\\hline\phantom{lll}&&&&1&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$18$$$'s are in $$$140$$$?

The answer is $$$7$$$.

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

Now, $$$140-18 \cdot 7 = 140 - 126= 14$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&7&.&7&7&\color{Chartreuse}{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&1&4&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&2&\phantom{.}&6\\\hline\phantom{lll}&&1&\phantom{.}&4&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&2&6\\\hline\phantom{lll}&&&&\color{Chartreuse}{1}&\color{Chartreuse}{4}&\color{Chartreuse}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&2&6\\\hline\phantom{lll}&&&&&1&4\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{500}{18}=27.7 \overline{7}$$$

Answer: $$$\frac{500}{18}=27.7\overline{7}$$$