Fraction to Decimal Calculator

Your input: convert $$$\frac{400}{27}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{4}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{4}&\phantom{8}&\phantom{1}&\phantom{4}\end{array}&\\27&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$27$$$'s are in $$$4$$$?

The answer is $$$0$$$.

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

Now, $$$4-27 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{Peru}{0}&\phantom{1}&\phantom{4}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{4}&\phantom{8}&\phantom{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{Peru}{4}& 0 \downarrow&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$27$$$'s are in $$$40$$$?

The answer is $$$1$$$.

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

Now, $$$40-27 \cdot 1 = 40 - 27= 13$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{BlueViolet}{1}&\phantom{4}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{4}&\phantom{8}&\phantom{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0& 0 \downarrow&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{4}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$27$$$'s are in $$$130$$$?

The answer is $$$4$$$.

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

Now, $$$130-27 \cdot 4 = 130 - 108= 22$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&1&\color{SaddleBrown}{4}&\phantom{.}&\phantom{8}&\phantom{1}&\phantom{4}&\phantom{8}&\phantom{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0&0&.& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{3}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&2&2&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$27$$$'s are in $$$220$$$?

The answer is $$$8$$$.

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

Now, $$$220-27 \cdot 8 = 220 - 216= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&1&4&.&\color{Green}{8}&\phantom{1}&\phantom{4}&\phantom{8}&\phantom{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0&0&.&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&\color{Green}{2}&\color{Green}{2}&\phantom{.}&\color{Green}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$27$$$'s are in $$$40$$$?

The answer is $$$1$$$.

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

Now, $$$40-27 \cdot 1 = 40 - 27= 13$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&1&4&.&8&\color{DarkBlue}{1}&\phantom{4}&\phantom{8}&\phantom{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0&0&.&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&2&2&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&&\color{DarkBlue}{4}&\color{DarkBlue}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&7\\\hline\phantom{lll}&&&&1&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$27$$$'s are in $$$130$$$?

The answer is $$$4$$$.

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

Now, $$$130-27 \cdot 4 = 130 - 108= 22$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&1&4&.&8&1&\color{DarkCyan}{4}&\phantom{8}&\phantom{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0&0&.&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&2&2&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&7\\\hline\phantom{lll}&&&&\color{DarkCyan}{1}&\color{DarkCyan}{3}&\color{DarkCyan}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&0&8\\\hline\phantom{lll}&&&&&2&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$27$$$'s are in $$$220$$$?

The answer is $$$8$$$.

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

Now, $$$220-27 \cdot 8 = 220 - 216= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&1&4&.&8&1&4&\color{Crimson}{8}&\phantom{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0&0&.&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&2&2&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&7\\\hline\phantom{lll}&&&&1&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&0&8\\\hline\phantom{lll}&&&&&\color{Crimson}{2}&\color{Crimson}{2}&\color{Crimson}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&1&6\\\hline\phantom{lll}&&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$27$$$'s are in $$$40$$$?

The answer is $$$1$$$.

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

Now, $$$40-27 \cdot 1 = 40 - 27= 13$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&1&4&.&8&1&4&8&\color{DeepPink}{1}&\phantom{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0&0&.&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&2&2&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&7\\\hline\phantom{lll}&&&&1&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&0&8\\\hline\phantom{lll}&&&&&2&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&1&6\\\hline\phantom{lll}&&&&&&&\color{DeepPink}{4}&\color{DeepPink}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&2&7\\\hline\phantom{lll}&&&&&&&1&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$27$$$'s are in $$$130$$$?

The answer is $$$4$$$.

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

Now, $$$130-27 \cdot 4 = 130 - 108= 22$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&1&4&.&8&1&4&8&1&\color{Red}{4}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}4&0&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&2&2&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&7\\\hline\phantom{lll}&&&&1&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&0&8\\\hline\phantom{lll}&&&&&2&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&1&6\\\hline\phantom{lll}&&&&&&&4&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&2&7\\\hline\phantom{lll}&&&&&&&\color{Red}{1}&\color{Red}{3}&\color{Red}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&0&8\\\hline\phantom{lll}&&&&&&&&2&2\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{400}{27}=14. \overline{814}$$$

Answer: $$$\frac{400}{27}=14.\overline{814}$$$