Fraction to Decimal Calculator

Your input: convert $$$\frac{400}{24}$$$ into a decimal.

Write the problem in the special format:

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

Step 1

How many $$$24$$$'s are in $$$4$$$?

The answer is $$$0$$$.

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

Now, $$$4-24 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

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

Step 2

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{DarkMagenta}{1}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}4&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{4}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&1&\color{DarkBlue}{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}4&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{6}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&1&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&1&6&.&\color{Purple}{6}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}4&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{1}&\color{Purple}{6}&\phantom{.}&\color{Purple}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&\phantom{.}&4\\\hline\phantom{lll}&&1&\phantom{.}&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&1&6&.&6&\color{DarkCyan}{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}4&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&1&6&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&\phantom{.}&4\\\hline\phantom{lll}&&\color{DarkCyan}{1}&\phantom{.}&\color{DarkCyan}{6}&\color{DarkCyan}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 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.

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

Step 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.

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

Step 8

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

The answer is $$$6$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&1&6&.&6&6&6&6&\color{BlueViolet}{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}4&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&1&6&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&\phantom{.}&4\\\hline\phantom{lll}&&1&\phantom{.}&6&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&1&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&\color{BlueViolet}{1}&\color{BlueViolet}{6}&\color{BlueViolet}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&4&4\\\hline\phantom{lll}&&&&&&&1&6\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{400}{24}=16.666 \overline{6}$$$

Answer: $$$\frac{400}{24}=16.666\overline{6}$$$