Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{1400}{18}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\18&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&4&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

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

Step 2

How many $$$18$$$'s are in $$$14$$$?

The answer is $$$0$$$.

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

Now, $$$14-18 \cdot 0 = 14 - 0= 14$$$.

Bring down the next digit of the dividend.

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

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.

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

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.

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

Step 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.

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

Step 6

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

The answer is $$$7$$$.

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

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

Bring down the next digit of the dividend.

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

Step 7

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

The answer is $$$7$$$.

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

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

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

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1400}{18}=77.7 \overline{7}$$$

Answer: $$$\frac{1400}{18}=77.7\overline{7}$$$