Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{2600}{40}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\40&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}2&6&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $40$'s are in $2$? The answer is $0$.

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

Now, $2-0 \cdot 40 = 2 - 0= 2$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Chartreuse}{0}&\phantom{0}&\phantom{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Chartreuse}{2}& 6 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $40$'s are in $26$? The answer is $0$.

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

Now, $26-0 \cdot 40 = 26 - 0= 26$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DeepPink}{0}&\phantom{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&6& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{2}&\color{DeepPink}{6}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $40$'s are in $260$? The answer is $6$.

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

Now, $260-6 \cdot 40 = 260 - 240= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{DarkMagenta}{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&6&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{2}&\color{DarkMagenta}{6}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&4&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $40$'s are in $200$? The answer is $5$.

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

Now, $200-5 \cdot 40 = 200 - 200= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{BlueViolet}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&6&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&4&0&\phantom{.}\\\hline\phantom{lll}&\color{BlueViolet}{2}&\color{BlueViolet}{0}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $40$'s are in $0$? The answer is $0$.

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

Now, $0-0 \cdot 40 = 0 - 0= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&5&.&\color{Red}{0}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&6&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&4&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Red}{0}&\phantom{.}&\color{Red}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

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

Therefore, $\frac{2600}{40}=65.0$

Answer: $\frac{2600}{40}=65.0$