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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.

Enter a fraction or

If you don't need a mixed number, leave the left cell empty.
If you need a negative fraction, write the minus sign in the left cell.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: convert 320055 into a decimal.

Write the problem in the special format:

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\55&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}3&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 1

How many 55's are in 3? The answer is 0.

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

Now, 3-0 \cdot 55 = 3 - 0= 3.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{DarkBlue}{0}&\phantom{0}&\phantom{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{DarkBlue}{3}& 2 \downarrow&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 2

How many 55's are in 32? The answer is 0.

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

Now, 32-0 \cdot 55 = 32 - 0= 32.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{Brown}{0}&\phantom{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{3}&\color{Brown}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 3

How many 55's are in 320? The answer is 5.

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

Now, 320-5 \cdot 55 = 320 - 275= 45.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&\color{SaddleBrown}{5}&\phantom{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{3}&\color{SaddleBrown}{2}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}

Step 4

How many 55's are in 450? The answer is 8.

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

Now, 450-8 \cdot 55 = 450 - 440= 10.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&\color{BlueViolet}{8}&\phantom{.}&\phantom{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&\color{BlueViolet}{4}&\color{BlueViolet}{5}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 5

How many 55's are in 100? The answer is 1.

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

Now, 100-1 \cdot 55 = 100 - 55= 45.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&\color{DeepPink}{1}&\phantom{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&\color{DeepPink}{1}&\color{DeepPink}{0}&\phantom{.}&\color{DeepPink}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 6

How many 55's are in 450? The answer is 8.

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

Now, 450-8 \cdot 55 = 450 - 440= 10.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&\color{OrangeRed}{8}&\phantom{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&\color{OrangeRed}{4}&\phantom{.}&\color{OrangeRed}{5}&\color{OrangeRed}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 7

How many 55's are in 100? The answer is 1.

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

Now, 100-1 \cdot 55 = 100 - 55= 45.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&8&\color{Blue}{1}&\phantom{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&\color{Blue}{1}&\color{Blue}{0}&\color{Blue}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&4&5&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 8

How many 55's are in 450? The answer is 8.

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

Now, 450-8 \cdot 55 = 450 - 440= 10.

Bring down the next digit of the dividend.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&8&1&\color{Green}{8}&\phantom{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&\color{Green}{4}&\color{Green}{5}&\color{Green}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&4&4&0\\\hline\phantom{lll}&&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}

Step 9

How many 55's are in 100? The answer is 1.

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

Now, 100-1 \cdot 55 = 100 - 55= 45.

\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&8&.&1&8&1&8&\color{GoldenRod}{1}\end{array}&\\\color{Magenta}{55}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}3&2&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&7&5&\phantom{.}\\\hline\phantom{lll}&4&5&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&4&4&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&5&5\\\hline\phantom{lll}&&&4&\phantom{.}&5&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&4&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&4&5&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&4&4&0\\\hline\phantom{lll}&&&&&&&\color{GoldenRod}{1}&\color{GoldenRod}{0}&\color{GoldenRod}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&5&5\\\hline\phantom{lll}&&&&&&&&4&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{3200}{55}=58.1 \overline{81}

Answer: \frac{3200}{55}=58.1\overline{81}