Fraction to Decimal Calculator

Your input: convert $$$\frac{1500}{33}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\33&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$33$$$'s are in $$$1$$$? The answer is $$$0$$$.

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

Now, $$$1-0 \cdot 33 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{DarkCyan}{0}&\phantom{0}&\phantom{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{DarkCyan}{1}& 5 \downarrow&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$33$$$'s are in $$$15$$$? The answer is $$$0$$$.

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

Now, $$$15-0 \cdot 33 = 15 - 0= 15$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{Peru}{0}&\phantom{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&5& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{1}&\color{Peru}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$33$$$'s are in $$$150$$$? The answer is $$$4$$$.

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

Now, $$$150-4 \cdot 33 = 150 - 132= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&\color{Red}{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&5&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Red}{1}&\color{Red}{5}&\color{Red}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&2&\phantom{.}\\\hline\phantom{lll}&1&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$33$$$'s are in $$$180$$$? The answer is $$$5$$$.

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

Now, $$$180-5 \cdot 33 = 180 - 165= 15$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&4&\color{Chartreuse}{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&5&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&2&\phantom{.}\\\hline\phantom{lll}&\color{Chartreuse}{1}&\color{Chartreuse}{8}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&6&5&\phantom{.}\\\hline\phantom{lll}&&1&5&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$33$$$'s are in $$$150$$$? The answer is $$$4$$$.

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

Now, $$$150-4 \cdot 33 = 150 - 132= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&4&5&.&\color{Chocolate}{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&5&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&2&\phantom{.}\\\hline\phantom{lll}&1&8&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&6&5&\phantom{.}\\\hline\phantom{lll}&&\color{Chocolate}{1}&\color{Chocolate}{5}&\phantom{.}&\color{Chocolate}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&3&\phantom{.}&2\\\hline\phantom{lll}&&&1&\phantom{.}&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$33$$$'s are in $$$180$$$? The answer is $$$5$$$.

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

Now, $$$180-5 \cdot 33 = 180 - 165= 15$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&4&5&.&4&\color{OrangeRed}{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&5&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&2&\phantom{.}\\\hline\phantom{lll}&1&8&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&6&5&\phantom{.}\\\hline\phantom{lll}&&1&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&3&\phantom{.}&2\\\hline\phantom{lll}&&&\color{OrangeRed}{1}&\phantom{.}&\color{OrangeRed}{8}&\color{OrangeRed}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&6&5\\\hline\phantom{lll}&&&&&1&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$33$$$'s are in $$$150$$$? The answer is $$$4$$$.

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

Now, $$$150-4 \cdot 33 = 150 - 132= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&4&5&.&4&5&\color{DeepPink}{4}&\phantom{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&5&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&2&\phantom{.}\\\hline\phantom{lll}&1&8&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&6&5&\phantom{.}\\\hline\phantom{lll}&&1&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&3&\phantom{.}&2\\\hline\phantom{lll}&&&1&\phantom{.}&8&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&6&5\\\hline\phantom{lll}&&&&&\color{DeepPink}{1}&\color{DeepPink}{5}&\color{DeepPink}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&3&2\\\hline\phantom{lll}&&&&&&1&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$33$$$'s are in $$$180$$$? The answer is $$$5$$$.

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

Now, $$$180-5 \cdot 33 = 180 - 165= 15$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&4&5&.&4&5&4&\color{Fuchsia}{5}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&5&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&2&\phantom{.}\\\hline\phantom{lll}&1&8&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&6&5&\phantom{.}\\\hline\phantom{lll}&&1&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&3&\phantom{.}&2\\\hline\phantom{lll}&&&1&\phantom{.}&8&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&6&5\\\hline\phantom{lll}&&&&&1&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&3&2\\\hline\phantom{lll}&&&&&&\color{Fuchsia}{1}&\color{Fuchsia}{8}&\color{Fuchsia}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&6&5\\\hline\phantom{lll}&&&&&&&1&5\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1500}{33}=45. \overline{45}$$$

Answer: $$$\frac{1500}{33}=45.\overline{45}$$$