Fraction to Decimal Calculator

Your input: convert $$$\frac{5500}{220}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\220&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}5&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$220$$$'s are in $$$5$$$? The answer is $$$0$$$.

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

Now, $$$5-0 \cdot 220 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{DarkCyan}{0}&\phantom{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{220}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{DarkCyan}{5}& 5 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$220$$$'s are in $$$55$$$? The answer is $$$0$$$.

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

Now, $$$55-0 \cdot 220 = 55 - 0= 55$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Peru}{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{220}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&5& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{5}&\color{Peru}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$220$$$'s are in $$$550$$$? The answer is $$$2$$$.

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

Now, $$$550-2 \cdot 220 = 550 - 440= 110$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Red}{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{220}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&5&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Red}{5}&\color{Red}{5}&\color{Red}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&4&0&\phantom{.}\\\hline\phantom{lll}1&1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$220$$$'s are in $$$1100$$$? The answer is $$$5$$$.

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

Now, $$$1100-5 \cdot 220 = 1100 - 1100= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&\color{Chartreuse}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{220}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&5&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&4&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{1}&\color{Chartreuse}{0}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&1&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$220$$$'s are in $$$0$$$? The answer is $$$0$$$.

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

Now, $$$0-0 \cdot 220 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&5&.&\color{Chocolate}{0}\end{array}&\\\color{Magenta}{220}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&5&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}4&4&0&\phantom{.}\\\hline\phantom{lll}1&1&0&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&1&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{5500}{220}=25.0 \overline{}$$$

Answer: $$$\frac{5500}{220}=25.0\overline{}$$$