Bruch-zu-Dezimal-Rechner
Schritt für Schritt Brüche in Dezimalzahlen umwandeln
Der Rechner wandelt den gegebenen (echten oder unechten) Bruch oder die gemischte Zahl in eine Dezimalzahl um (eventuell mit Wiederholungen oder wiederkehrenden Zahlen), wobei die Schritte angezeigt werden.
Solution
Your input: convert 320055 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{Violet}{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{Violet}{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{Green}{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{Green}{3}&\color{Green}{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{DarkCyan}{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{DarkCyan}{3}&\color{DarkCyan}{2}&\color{DarkCyan}{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{Chartreuse}{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{Chartreuse}{4}&\color{Chartreuse}{5}&\color{Chartreuse}{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{Chocolate}{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{Chocolate}{1}&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{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{Brown}{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{Brown}{4}&\phantom{.}&\color{Brown}{5}&\color{Brown}{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{Crimson}{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{Crimson}{1}&\color{Crimson}{0}&\color{Crimson}{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{OrangeRed}{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{OrangeRed}{4}&\color{OrangeRed}{5}&\color{OrangeRed}{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{DarkBlue}{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{DarkBlue}{1}&\color{DarkBlue}{0}&\color{DarkBlue}{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}