Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{1800}{80}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{2}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\80&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&8&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$80$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-80 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{DeepPink}{0}&\phantom{0}&\phantom{2}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{80}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{DeepPink}{1}& 8 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$80$$$'s are in $$$18$$$?

The answer is $$$0$$$.

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

Now, $$$18-80 \cdot 0 = 18 - 0= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{SaddleBrown}{0}&\phantom{2}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{80}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{8}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$80$$$'s are in $$$180$$$?

The answer is $$$2$$$.

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

Now, $$$180-80 \cdot 2 = 180 - 160= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Chartreuse}{2}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{80}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{8}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$80$$$'s are in $$$200$$$?

The answer is $$$2$$$.

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

Now, $$$200-80 \cdot 2 = 200 - 160= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&\color{Brown}{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{80}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&\phantom{.}\\\hline\phantom{lll}&\color{Brown}{2}&\color{Brown}{0}&\color{Brown}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&6&0&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$80$$$'s are in $$$400$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$400-80 \cdot 5 = 400 - 400= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&2&.&\color{Crimson}{5}\end{array}&\\\color{Magenta}{80}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&6&0&\phantom{.}\\\hline\phantom{lll}&&\color{Crimson}{4}&\color{Crimson}{0}&\phantom{.}&\color{Crimson}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&4&0&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{1800}{80}=22.5$$$

Answer: $$$\frac{1800}{80}=22.5$$$