Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{1200}{25}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\25&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $25$'s are in $1$? The answer is $0$.

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

Now, $1-0 \cdot 25 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{OrangeRed}{0}&\phantom{0}&\phantom{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{OrangeRed}{1}& 2 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $25$'s are in $12$? The answer is $0$.

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

Now, $12-0 \cdot 25 = 12 - 0= 12$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Violet}{0}&\phantom{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{1}&\color{Violet}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $25$'s are in $120$? The answer is $4$.

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

Now, $120-4 \cdot 25 = 120 - 100= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Peru}{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{1}&\color{Peru}{2}&\color{Peru}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $25$'s are in $200$? The answer is $8$.

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

Now, $200-8 \cdot 25 = 200 - 200= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&\color{Chocolate}{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{2}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $25$'s are in $0$? The answer is $0$.

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

Now, $0-0 \cdot 25 = 0 - 0= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&8&.&\color{DeepPink}{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{DeepPink}{0}&\phantom{.}&\color{DeepPink}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

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

Therefore, $\frac{1200}{25}=48.0$

Answer: $\frac{1200}{25}=48.0$