Fraction to Decimal Calculator

Your input: convert $$$\frac{12400}{150}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{8}&\phantom{2}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\150&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&2&4&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{Chartreuse}{0}&\phantom{0}&\phantom{0}&\phantom{8}&\phantom{2}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{Chartreuse}{1}& 2 \downarrow&4&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$150$$$'s are in $$$12$$$?

The answer is $$$0$$$.

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

Now, $$$12-150 \cdot 0 = 12 - 0= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{Green}{0}&\phantom{0}&\phantom{8}&\phantom{2}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&2& 4 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{2}&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&4&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$150$$$'s are in $$$124$$$?

The answer is $$$0$$$.

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

Now, $$$124-150 \cdot 0 = 124 - 0= 124$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&\color{Purple}{0}&\phantom{8}&\phantom{2}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&2&4& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{2}&\color{Purple}{4}&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$150$$$'s are in $$$1240$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$1240-150 \cdot 8 = 1240 - 1200= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&\color{Violet}{8}&\phantom{2}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&2&4&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&4&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{1}&\color{Violet}{2}&\color{Violet}{4}&\color{Violet}{0}&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&4&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$150$$$'s are in $$$400$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$400-150 \cdot 2 = 400 - 300= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&8&\color{Brown}{2}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&2&4&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&4&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&4&0&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{4}&\color{Brown}{0}&\color{Brown}{0}&\phantom{.}\\&-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&8&2&.&\color{Blue}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&2&4&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&4&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&4&0&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&4&0&0&\phantom{.}\\&-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{1}&\color{Blue}{0}&\color{Blue}{0}&\phantom{.}&\color{Blue}{0}\\&-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0&0\\\hline\phantom{lll}&&&1&0&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&8&2&.&6&\color{Peru}{6}&\phantom{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&2&4&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&4&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&4&0&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&4&0&0&\phantom{.}\\&-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\\&-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0&0\\\hline\phantom{lll}&&&\color{Peru}{1}&\color{Peru}{0}&\phantom{.}&\color{Peru}{0}&\color{Peru}{0}\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&9&0&\phantom{.}&0\\\hline\phantom{lll}&&&&1&\phantom{.}&0&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

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

The answer is $$$6$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&0&8&2&.&6&6&\color{Fuchsia}{6}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&2&4&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&4&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&4&0&\phantom{.}\\-&\phantom{2}&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&4&0&0&\phantom{.}\\&-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\\&-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0&0\\\hline\phantom{lll}&&&1&0&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&9&0&\phantom{.}&0\\\hline\phantom{lll}&&&&\color{Fuchsia}{1}&\phantom{.}&\color{Fuchsia}{0}&\color{Fuchsia}{0}&\color{Fuchsia}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&9&\phantom{.}&0&0\\\hline\phantom{lll}&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{12400}{150}=82.6 \overline{6}$$$

Answer: $$$\frac{12400}{150}=82.6\overline{6}$$$