Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{11500}{125}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\125&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&1&5&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{0}&\phantom{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Fuchsia}{1}& 1 \downarrow&5&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$125$$$'s are in $$$11$$$?

The answer is $$$0$$$.

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

Now, $$$11-125 \cdot 0 = 11 - 0= 11$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Chocolate}{0}&\phantom{0}&\phantom{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&1& 5 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{1}&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$125$$$'s are in $$$115$$$?

The answer is $$$0$$$.

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

Now, $$$115-125 \cdot 0 = 115 - 0= 115$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{SaddleBrown}{0}&\phantom{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&1&5& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{1}&\color{SaddleBrown}{5}&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$125$$$'s are in $$$1150$$$?

The answer is $$$9$$$.

Write down $$$9$$$ in the upper part of the table.

Now, $$$1150-125 \cdot 9 = 1150 - 1125= 25$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Chartreuse}{9}&\phantom{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&1&5&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{1}&\color{Chartreuse}{5}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&1&2&5&\phantom{.}\\\hline\phantom{lll}&&2&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$125$$$'s are in $$$250$$$?

The answer is $$$2$$$.

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

Now, $$$250-125 \cdot 2 = 250 - 250= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&9&\color{Blue}{2}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&1&5&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&1&2&5&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{2}&\color{Blue}{5}&\color{Blue}{0}&\phantom{.}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&2&5&0&\phantom{.}\\\hline\phantom{lll}&&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

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

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&9&2&.&\color{DarkBlue}{0}\end{array}&\\\color{Magenta}{125}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&1&5&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&1&2&5&\phantom{.}\\\hline\phantom{lll}&&2&5&0&\phantom{.}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&2&5&0&\phantom{.}\\\hline\phantom{lll}&&&&\color{DarkBlue}{0}&\phantom{.}&\color{DarkBlue}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{11500}{125}=92.0$$$

Answer: $$$\frac{11500}{125}=92.0$$$