Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{10000}{125}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\125&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&0&0&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$125$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-125 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{DarkCyan}{0}&\phantom{0}&\phantom{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{DarkCyan}{1}& 0 \downarrow&0&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$125$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-125 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Blue}{0}&\phantom{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0& 0 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{1}&\color{Blue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$125$$$'s are in $$$100$$$?

The answer is $$$0$$$.

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

Now, $$$100-125 \cdot 0 = 100 - 0= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Chocolate}{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&0&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$125$$$'s are in $$$1000$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$1000-125 \cdot 8 = 1000 - 1000= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Peru}{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{1}&\color{Peru}{0}&\color{Peru}{0}&\color{Peru}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$125$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-125 \cdot 0 = 0 - 0= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&\color{DarkBlue}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&0&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{DarkBlue}{0}&\color{DarkBlue}{0}&\phantom{.}\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&0&\phantom{.}\\\hline\phantom{lll}&&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$125$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-125 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&0&.&\color{Red}{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&0&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&0&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&0&\phantom{.}\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&0&\phantom{.}\\\hline\phantom{lll}&&&&\color{Red}{0}&\phantom{.}&\color{Red}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{10000}{125}=80.0$$$

Answer: $$$\frac{10000}{125}=80.0$$$