Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{1000}{24}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{4}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\24&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&0&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$24$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-24 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{4}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{Fuchsia}{1}& 0 \downarrow&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$24$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-24 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{Red}{0}&\phantom{4}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Red}{1}&\color{Red}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$24$$$'s are in $$$100$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$100-24 \cdot 4 = 100 - 96= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&\color{Green}{4}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{0}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$24$$$'s are in $$$40$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$40-24 \cdot 1 = 40 - 24= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&4&\color{Peru}{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&\color{Peru}{4}&\color{Peru}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

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

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&4&1&.&\color{SaddleBrown}{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&4&\phantom{.}\\\hline\phantom{lll}&&\color{SaddleBrown}{1}&\color{SaddleBrown}{6}&\phantom{.}&\color{SaddleBrown}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

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

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&4&1&.&6&\color{Chartreuse}{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&\color{Chartreuse}{1}&\phantom{.}&\color{Chartreuse}{6}&\color{Chartreuse}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

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

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&4&1&.&6&6&\color{OrangeRed}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&\color{OrangeRed}{1}&\color{OrangeRed}{6}&\color{OrangeRed}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

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

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&4&1&.&6&6&6&\color{Violet}{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&\color{Violet}{1}&\color{Violet}{6}&\color{Violet}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&4&4\\\hline\phantom{lll}&&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

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

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&4&1&.&6&6&6&6&\color{GoldenRod}{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&1&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&4&4\\\hline\phantom{lll}&&&&&&&\color{GoldenRod}{1}&\color{GoldenRod}{6}&\color{GoldenRod}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&4&4\\\hline\phantom{lll}&&&&&&&&1&6\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1000}{24}=41.666 \overline{6}$$$

Answer: $$$\frac{1000}{24}=41.666\overline{6}$$$