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Bruch-zu-Dezimalzahl-Rechner
Brüche Schritt für Schritt in Dezimalzahlen umwandeln
Der Rechner wandelt den gegebenen Bruch (echt oder unecht) oder die gemischte Zahl in eine Dezimalzahl um (möglicherweise periodisch/repetierend) und zeigt die Rechenschritte an.
Solution
Your input: convert $$$\frac{1800}{30}$$$ into a decimal.
Write the problem in the special format:
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&8&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 1
How many $$$30$$$'s are in $$$1$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$1-30 \cdot 0 = 1 - 0= 1$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Fuchsia}{1}& 8 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 2
How many $$$30$$$'s are in $$$18$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$18-30 \cdot 0 = 18 - 0= 18$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Chocolate}{0}&\phantom{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{8}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 3
How many $$$30$$$'s are in $$$180$$$?
The answer is $$$6$$$.
Write down $$$6$$$ in the upper part of the table.
Now, $$$180-30 \cdot 6 = 180 - 180= 0$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Purple}{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{8}&\color{Purple}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 4
How many $$$30$$$'s are in $$$0$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$0-30 \cdot 0 = 0 - 0= 0$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{OrangeRed}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&&\color{OrangeRed}{0}&\color{OrangeRed}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 5
How many $$$30$$$'s are in $$$0$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$0-30 \cdot 0 = 0 - 0= 0$$$.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&0&.&\color{DarkMagenta}{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&8&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{DarkMagenta}{0}&\phantom{.}&\color{DarkMagenta}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1800}{30}=60. \overline{0}$$$
Answer: $$$\frac{1800}{30}=60.\overline{0}$$$