Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{2100}{30}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}2&1&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $30$'s are in $2$? The answer is $0$.

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

Now, $2-0 \cdot 30 = 2 - 0= 2$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Blue}{0}&\phantom{0}&\phantom{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Blue}{2}& 1 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $30$'s are in $21$? The answer is $0$.

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

Now, $21-0 \cdot 30 = 21 - 0= 21$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Purple}{0}&\phantom{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{2}&\color{Purple}{1}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $30$'s are in $210$? The answer is $7$.

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

Now, $210-7 \cdot 30 = 210 - 210= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Peru}{7}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{2}&\color{Peru}{1}&\color{Peru}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&1&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $30$'s are in $0$? The answer is $0$.

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

Now, $0-0 \cdot 30 = 0 - 0= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&\color{Green}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&1&0&\phantom{.}\\\hline\phantom{lll}&&\color{Green}{0}&\color{Green}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $30$'s are in $0$? The answer is $0$.

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

Now, $0-0 \cdot 30 = 0 - 0= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&7&0&.&\color{DarkMagenta}{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&1&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&1&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{DarkMagenta}{0}&\phantom{.}&\color{DarkMagenta}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{2100}{30}=70. \overline{0}$

Answer: $\frac{2100}{30}=70.\overline{0}$