Fraction to Decimal Calculator
Convert fractions to decimals step by step
The calculator will convert the given fraction (proper or improper) or mixed number into a decimal (possibly, repeating or recurring), with steps shown.
Solution
Your input: convert $$$\frac{500}{9}$$$ into a decimal.
Write the problem in the special format:
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{5}&\phantom{5}&\phantom{.}&\phantom{5}&\phantom{5}\end{array}&\\9&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}5&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 1
How many $$$9$$$'s are in $$$5$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$5-9 \cdot 0 = 5 - 0= 5$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Chartreuse}{0}&\phantom{5}&\phantom{5}&\phantom{.}&\phantom{5}&\phantom{5}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Chartreuse}{5}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 2
How many $$$9$$$'s are in $$$50$$$?
The answer is $$$5$$$.
Write down $$$5$$$ in the upper part of the table.
Now, $$$50-9 \cdot 5 = 50 - 45= 5$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Green}{5}&\phantom{5}&\phantom{.}&\phantom{5}&\phantom{5}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{5}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}4&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 3
How many $$$9$$$'s are in $$$50$$$?
The answer is $$$5$$$.
Write down $$$5$$$ in the upper part of the table.
Now, $$$50-9 \cdot 5 = 50 - 45= 5$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&\color{Purple}{5}&\phantom{.}&\phantom{5}&\phantom{5}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}4&5&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{5}&\color{Purple}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 4
How many $$$9$$$'s are in $$$50$$$?
The answer is $$$5$$$.
Write down $$$5$$$ in the upper part of the table.
Now, $$$50-9 \cdot 5 = 50 - 45= 5$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&5&.&\color{Violet}{5}&\phantom{5}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}4&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&5&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{5}&\phantom{.}&\color{Violet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&5\\\hline\phantom{lll}&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 5
How many $$$9$$$'s are in $$$50$$$?
The answer is $$$5$$$.
Write down $$$5$$$ in the upper part of the table.
Now, $$$50-9 \cdot 5 = 50 - 45= 5$$$.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&5&5&.&5&\color{Brown}{5}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}4&5&\phantom{.}\\\hline\phantom{lll}&5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&5\\\hline\phantom{lll}&&&&\color{Brown}{5}&\color{Brown}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&4&5\\\hline\phantom{lll}&&&&&5\end{array}&\begin{array}{c}\end{array}\end{array}$$$
As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{500}{9}=55. \overline{5}$$$
Answer: $$$\frac{500}{9}=55.\overline{5}$$$