Fraction to Decimal Calculator

Your input: convert $$$\frac{12000}{150}$$$ into a decimal.

Write the problem in the special format:

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

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Fuchsia}{1}& 2 \downarrow&0&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Peru}{0}&\phantom{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2& 0 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{1}&\color{Peru}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$150$$$'s are in $$$120$$$?

The answer is $$$0$$$.

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

Now, $$$120-150 \cdot 0 = 120 - 0= 120$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{DeepPink}{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&0& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{1}&\color{DeepPink}{2}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$150$$$'s are in $$$1200$$$?

The answer is $$$8$$$.

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

Now, $$$1200-150 \cdot 8 = 1200 - 1200= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Chocolate}{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&0&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{2}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$150$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

Bring down the next digit of the dividend.

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

Step 6

How many $$$150$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&0&.&\color{OrangeRed}{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&0&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&0&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&0&\phantom{.}\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&0&\phantom{.}\\\hline\phantom{lll}&&&&\color{OrangeRed}{0}&\phantom{.}&\color{OrangeRed}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{12000}{150}=80.0 \overline{}$$$

Answer: $$$\frac{12000}{150}=80.0\overline{}$$$