Fraction to Decimal Calculator

Your input: convert $$$\frac{400}{9}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{4}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}\end{array}&\\9&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$9$$$'s are in $$$4$$$?

The answer is $$$0$$$.

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

Now, $$$4-9 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Red}{0}&\phantom{4}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Red}{4}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$9$$$'s are in $$$40$$$?

The answer is $$$4$$$.

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

Now, $$$40-9 \cdot 4 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Chartreuse}{4}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{4}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$9$$$'s are in $$$40$$$?

The answer is $$$4$$$.

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

Now, $$$40-9 \cdot 4 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&4&\color{Violet}{4}&\phantom{.}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}&\color{Violet}{4}&\color{Violet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$9$$$'s are in $$$40$$$?

The answer is $$$4$$$.

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

Now, $$$40-9 \cdot 4 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&4&4&.&\color{Peru}{4}&\phantom{4}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&6&\phantom{.}\\\hline\phantom{lll}&&\color{Peru}{4}&\phantom{.}&\color{Peru}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$9$$$'s are in $$$40$$$?

The answer is $$$4$$$.

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

Now, $$$40-9 \cdot 4 = 40 - 36= 4$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&4&4&.&4&\color{DarkMagenta}{4}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&\color{DarkMagenta}{4}&\color{DarkMagenta}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&6\\\hline\phantom{lll}&&&&&4\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{400}{9}=44. \overline{4}$$$

Answer: $$$\frac{400}{9}=44.\overline{4}$$$