Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{6500}{100}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\100&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}6&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$100$$$'s are in $$$6$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$6-100 \cdot 0 = 6 - 0= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{SaddleBrown}{0}&\phantom{0}&\phantom{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{SaddleBrown}{6}& 5 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$100$$$'s are in $$$65$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$65-100 \cdot 0 = 65 - 0= 65$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Brown}{0}&\phantom{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&5& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{6}&\color{Brown}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}6&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$100$$$'s are in $$$650$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$650-100 \cdot 6 = 650 - 600= 50$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{DarkCyan}{6}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&5&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{6}&\color{DarkCyan}{5}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&0&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$100$$$'s are in $$$500$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$500-100 \cdot 5 = 500 - 500= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{Peru}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&5&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}6&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&0&0&\phantom{.}\\\hline\phantom{lll}&\color{Peru}{5}&\color{Peru}{0}&\color{Peru}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&5&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$100$$$'s are in $$$0$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$0-100 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&5&.&\color{Violet}{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&5&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}6&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&0&0&\phantom{.}\\\hline\phantom{lll}&5&0&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&5&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Violet}{0}&\phantom{.}&\color{Violet}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{6500}{100}=65.0$$$

Answer: $$$\frac{6500}{100}=65.0$$$