Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{2200}{32}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{8}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\32&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}2&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$32$$$'s are in $$$2$$$?

The answer is $$$0$$$.

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

Now, $$$2-32 \cdot 0 = 2 - 0= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Chartreuse}{0}&\phantom{0}&\phantom{6}&\phantom{8}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Chartreuse}{2}& 2 \downarrow&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$32$$$'s are in $$$22$$$?

The answer is $$$0$$$.

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

Now, $$$22-32 \cdot 0 = 22 - 0= 22$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Green}{0}&\phantom{6}&\phantom{8}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&2& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{2}&\color{Green}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$32$$$'s are in $$$220$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$220-32 \cdot 6 = 220 - 192= 28$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Purple}{6}&\phantom{8}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&2&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{2}&\color{Purple}{2}&\color{Purple}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&9&2&\phantom{.}\\\hline\phantom{lll}&2&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$32$$$'s are in $$$280$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$280-32 \cdot 8 = 280 - 256= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&\color{Violet}{8}&\phantom{.}&\phantom{7}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&2&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&9&2&\phantom{.}\\\hline\phantom{lll}&\color{Violet}{2}&\color{Violet}{8}&\color{Violet}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&5&6&\phantom{.}\\\hline\phantom{lll}&&2&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$32$$$'s are in $$$240$$$?

The answer is $$$7$$$.

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

Now, $$$240-32 \cdot 7 = 240 - 224= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&8&.&\color{Brown}{7}&\phantom{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&2&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&9&2&\phantom{.}\\\hline\phantom{lll}&2&8&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&5&6&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{2}&\color{Brown}{4}&\phantom{.}&\color{Brown}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&2&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$32$$$'s are in $$$160$$$?

The answer is $$$5$$$.

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

Now, $$$160-32 \cdot 5 = 160 - 160= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&8&.&7&\color{Blue}{5}\end{array}&\\\color{Magenta}{32}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&2&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&9&2&\phantom{.}\\\hline\phantom{lll}&2&8&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&5&6&\phantom{.}\\\hline\phantom{lll}&&2&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&2&\phantom{.}&4\\\hline\phantom{lll}&&&\color{Blue}{1}&\phantom{.}&\color{Blue}{6}&\color{Blue}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&6&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{2200}{32}=68.75$$$

Answer: $$$\frac{2200}{32}=68.75$$$