Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{3200}{55}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\55&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}3&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $55$'s are in $3$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $3-0 \cdot 55 = 3 - 0= 3$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{OrangeRed}{0}&\phantom{0}&\phantom{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{OrangeRed}{3}& 2 \downarrow&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $55$'s are in $32$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $32-0 \cdot 55 = 32 - 0= 32$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{Violet}{0}&\phantom{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{3}&\color{Violet}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $55$'s are in $320$? The answer is $5$.

Write down the calculated result in the upper part of the table.

Now, $320-5 \cdot 55 = 320 - 275= 45$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&\color{DeepPink}{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{3}&\color{DeepPink}{2}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $55$'s are in $450$? The answer is $8$.

Write down the calculated result in the upper part of the table.

Now, $450-8 \cdot 55 = 450 - 440= 10$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&\color{Brown}{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&\color{Brown}{4}&\color{Brown}{5}&\color{Brown}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $55$'s are in $100$? The answer is $1$.

Write down the calculated result in the upper part of the table.

Now, $100-1 \cdot 55 = 100 - 55= 45$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&\color{DarkBlue}{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&\color{DarkBlue}{1}&\color{DarkBlue}{0}&\phantom{.}&\color{DarkBlue}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $55$'s are in $450$? The answer is $8$.

Write down the calculated result in the upper part of the table.

Now, $450-8 \cdot 55 = 450 - 440= 10$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&\color{Chartreuse}{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&\color{Chartreuse}{4}&\phantom{.}&\color{Chartreuse}{5}&\color{Chartreuse}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 7

How many $55$'s are in $100$? The answer is $1$.

Write down the calculated result in the upper part of the table.

Now, $100-1 \cdot 55 = 100 - 55= 45$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&8&\color{Red}{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&\color{Red}{1}&\color{Red}{0}&\color{Red}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&4&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 8

How many $55$'s are in $450$? The answer is $8$.

Write down the calculated result in the upper part of the table.

Now, $450-8 \cdot 55 = 450 - 440= 10$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&8&1&\color{DarkCyan}{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&\color{DarkCyan}{4}&\color{DarkCyan}{5}&\color{DarkCyan}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&4&4&0\\\hline\phantom{lll}&&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 9

How many $55$'s are in $100$? The answer is $1$.

Write down the calculated result in the upper part of the table.

Now, $100-1 \cdot 55 = 100 - 55= 45$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&8&1&8&\color{Purple}{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&4&5&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&4&4&0\\\hline\phantom{lll}&&&&&&&\color{Purple}{1}&\color{Purple}{0}&\color{Purple}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&5&5\\\hline\phantom{lll}&&&&&&&&4&5\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{3200}{55}=58.1 \overline{81}$

Answer: $\frac{3200}{55}=58.1\overline{81}$