Fraction to Decimal Calculator

Your input: convert $\frac{500}{18}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\18&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}5&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $18$'s are in $5$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $5-0 \cdot 18 = 5 - 0= 5$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Green}{0}&\phantom{2}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Green}{5}& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $18$'s are in $50$? The answer is $2$.

Write down the calculated result in the upper part of the table.

Now, $50-2 \cdot 18 = 50 - 36= 14$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{GoldenRod}{2}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{5}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $18$'s are in $140$? The answer is $7$.

Write down the calculated result in the upper part of the table.

Now, $140-7 \cdot 18 = 140 - 126= 14$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&\color{DarkBlue}{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{4}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&1&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $18$'s are in $140$? The answer is $7$.

Write down the calculated result in the upper part of the table.

Now, $140-7 \cdot 18 = 140 - 126= 14$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&7&.&\color{DeepPink}{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&\color{DeepPink}{1}&\color{DeepPink}{4}&\phantom{.}&\color{DeepPink}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&2&\phantom{.}&6\\\hline\phantom{lll}&&1&\phantom{.}&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $18$'s are in $140$? The answer is $7$.

Write down the calculated result in the upper part of the table.

Now, $140-7 \cdot 18 = 140 - 126= 14$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&7&.&7&\color{Fuchsia}{7}&\phantom{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&1&4&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&2&\phantom{.}&6\\\hline\phantom{lll}&&\color{Fuchsia}{1}&\phantom{.}&\color{Fuchsia}{4}&\color{Fuchsia}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&2&6\\\hline\phantom{lll}&&&&1&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $18$'s are in $140$? The answer is $7$.

Write down the calculated result in the upper part of the table.

Now, $140-7 \cdot 18 = 140 - 126= 14$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&2&7&.&7&7&\color{DarkCyan}{7}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}5&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&6&\phantom{.}\\\hline\phantom{lll}&1&4&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&2&\phantom{.}&6\\\hline\phantom{lll}&&1&\phantom{.}&4&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&2&6\\\hline\phantom{lll}&&&&\color{DarkCyan}{1}&\color{DarkCyan}{4}&\color{DarkCyan}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&2&6\\\hline\phantom{lll}&&&&&1&4\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{500}{18}=27.7 \overline{7}$

Answer: $\frac{500}{18}=27.7\overline{7}$