Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{4800}{25}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{1}&\phantom{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\25&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&8&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $25$'s are in $4$? The answer is $0$.

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

Now, $4-0 \cdot 25 = 4 - 0= 4$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Brown}{0}&\phantom{1}&\phantom{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Brown}{4}& 8 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&8&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $25$'s are in $48$? The answer is $1$.

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

Now, $48-1 \cdot 25 = 48 - 25= 23$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Violet}{1}&\phantom{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&8& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{4}&\color{Violet}{8}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&5&\phantom{.}\\\hline\phantom{lll}2&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $25$'s are in $230$? The answer is $9$.

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

Now, $230-9 \cdot 25 = 230 - 225= 5$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&1&\color{Crimson}{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&8&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&5&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{2}&\color{Crimson}{3}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&2&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $25$'s are in $50$? The answer is $2$.

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

Now, $50-2 \cdot 25 = 50 - 50= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&1&9&\color{Red}{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&8&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&5&\phantom{.}\\\hline\phantom{lll}2&3&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&2&5&\phantom{.}\\\hline\phantom{lll}&&\color{Red}{5}&\color{Red}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&5&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

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

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&1&9&2&.&\color{Peru}{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&8&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&5&\phantom{.}\\\hline\phantom{lll}2&3&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&2&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&5&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Peru}{0}&\phantom{.}&\color{Peru}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

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

Therefore, $\frac{4800}{25}=192.0$

Answer: $\frac{4800}{25}=192.0$