Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{1200}{5}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{2}&\phantom{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\5&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$5$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-5 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{DarkBlue}{0}&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{DarkBlue}{1}& 2 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$5$$$'s are in $$$12$$$?

The answer is $$$2$$$.

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

Now, $$$12-5 \cdot 2 = 12 - 10= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Chocolate}{2}&\phantom{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$5$$$'s are in $$$20$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$20-5 \cdot 4 = 20 - 20= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&2&\color{DarkMagenta}{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkMagenta}{2}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$5$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&2&4&\color{Violet}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{0}&\color{Violet}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$5$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&2&4&0&.&\color{Brown}{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Brown}{0}&\phantom{.}&\color{Brown}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Since the remainder is $$$0$$$, then we are done.

Therefore, $$$\frac{1200}{5}=240.0$$$

Answer: $$$\frac{1200}{5}=240.0$$$