Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{500}{8}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{6}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\8&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}5&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$8$$$'s are in $$$5$$$?

The answer is $$$0$$$.

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

Now, $$$5-8 \cdot 0 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Blue}{0}&\phantom{6}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{8}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Blue}{5}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$8$$$'s are in $$$50$$$?

The answer is $$$6$$$.

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

Now, $$$50-8 \cdot 6 = 50 - 48= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{Fuchsia}{6}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{8}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}5&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Fuchsia}{5}&\color{Fuchsia}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$8$$$'s are in $$$20$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$20-8 \cdot 2 = 20 - 16= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&6&\color{OrangeRed}{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{8}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}5&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&8&\phantom{.}\\\hline\phantom{lll}&\color{OrangeRed}{2}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$8$$$'s are in $$$40$$$?

The answer is $$$5$$$.

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

Now, $$$40-8 \cdot 5 = 40 - 40= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&6&2&.&\color{Purple}{5}\end{array}&\\\color{Magenta}{8}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}5&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&6&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{4}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{500}{8}=62.5$$$

Answer: $$$\frac{500}{8}=62.5$$$