Fraction to Decimal Calculator

Your input: convert $$$\frac{11500}{150}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{7}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\150&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&1&5&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$150$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-150 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{Brown}{0}&\phantom{0}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{Brown}{1}& 1 \downarrow&5&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$150$$$'s are in $$$11$$$?

The answer is $$$0$$$.

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

Now, $$$11-150 \cdot 0 = 11 - 0= 11$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{Crimson}{0}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1& 5 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{1}&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$150$$$'s are in $$$115$$$?

The answer is $$$0$$$.

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

Now, $$$115-150 \cdot 0 = 115 - 0= 115$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&\color{Red}{0}&\phantom{7}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&5& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Red}{1}&\color{Red}{1}&\color{Red}{5}&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$150$$$'s are in $$$1150$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$1150-150 \cdot 7 = 1150 - 1050= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&\color{GoldenRod}{7}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&5&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{1}&\color{GoldenRod}{1}&\color{GoldenRod}{5}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$150$$$'s are in $$$1000$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$1000-150 \cdot 6 = 1000 - 900= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&7&\color{BlueViolet}{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&5&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&0&\phantom{.}\\\hline\phantom{lll}&\color{BlueViolet}{1}&\color{BlueViolet}{0}&\color{BlueViolet}{0}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$150$$$'s are in $$$1000$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$1000-150 \cdot 6 = 1000 - 900= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&7&6&.&\color{Chocolate}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&5&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{Chocolate}{1}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{0}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0&0\\\hline\phantom{lll}&&&1&0&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$150$$$'s are in $$$1000$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$1000-150 \cdot 6 = 1000 - 900= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&7&6&.&6&\color{Peru}{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&5&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0&0\\\hline\phantom{lll}&&&\color{Peru}{1}&\color{Peru}{0}&\phantom{.}&\color{Peru}{0}&\color{Peru}{0}\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&9&0&\phantom{.}&0\\\hline\phantom{lll}&&&&1&\phantom{.}&0&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$150$$$'s are in $$$1000$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$1000-150 \cdot 6 = 1000 - 900= 100$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&7&6&.&6&6&\color{DeepPink}{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&5&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&5&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&1&5&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&0&\phantom{.}\\-&\phantom{1}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0&0\\\hline\phantom{lll}&&&1&0&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&9&0&\phantom{.}&0\\\hline\phantom{lll}&&&&\color{DeepPink}{1}&\phantom{.}&\color{DeepPink}{0}&\color{DeepPink}{0}&\color{DeepPink}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&9&\phantom{.}&0&0\\\hline\phantom{lll}&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{11500}{150}=76.6 \overline{6}$$$

Answer: $$$\frac{11500}{150}=76.6\overline{6}$$$