Calculadora de Fração para Decimal

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 $$$0$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

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

Step 2

How many $$$33$$$'s are in $$$15$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

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

Step 3

How many $$$33$$$'s are in $$$150$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

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

Step 4

How many $$$33$$$'s are in $$$180$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

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

Step 5

How many $$$33$$$'s are in $$$150$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

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

Step 6

How many $$$33$$$'s are in $$$180$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

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

Step 7

How many $$$33$$$'s are in $$$150$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

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

Step 8

How many $$$33$$$'s are in $$$180$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

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

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

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