Fraction to Decimal Calculator

Your input: convert $\frac{500}{11}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\11&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}5&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $11$'s are in $5$? The answer is $0$.

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

Now, $5-0 \cdot 11 = 5 - 0= 5$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{DeepPink}{0}&\phantom{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{DeepPink}{5}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $11$'s are in $50$? The answer is $4$.

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

Now, $50-4 \cdot 11 = 50 - 44= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Peru}{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{5}&\color{Peru}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $11$'s are in $60$? The answer is $5$.

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

Now, $60-5 \cdot 11 = 60 - 55= 5$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&\color{Blue}{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&\color{Blue}{6}&\color{Blue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $11$'s are in $50$? The answer is $4$.

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

Now, $50-4 \cdot 11 = 50 - 44= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&\color{Fuchsia}{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&\color{Fuchsia}{5}&\phantom{.}&\color{Fuchsia}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $11$'s are in $60$? The answer is $5$.

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

Now, $60-5 \cdot 11 = 60 - 55= 5$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&4&\color{Brown}{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&\color{Brown}{6}&\color{Brown}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&5\\\hline\phantom{lll}&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $11$'s are in $50$? The answer is $4$.

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

Now, $50-4 \cdot 11 = 50 - 44= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&4&5&\color{Purple}{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&5\\\hline\phantom{lll}&&&&&\color{Purple}{5}&\color{Purple}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 7

How many $11$'s are in $60$? The answer is $5$.

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

Now, $60-5 \cdot 11 = 60 - 55= 5$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&4&5&4&\color{Red}{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&5\\\hline\phantom{lll}&&&&&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&&\color{Red}{6}&\color{Red}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&&5\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{500}{11}=45. \overline{45}$

Answer: $\frac{500}{11}=45.\overline{45}$