Fraction to Decimal Calculator

Your input: convert $$$\frac{10500}{120}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{8}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\120&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&0&5&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$120$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-120 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Brown}{0}&\phantom{0}&\phantom{0}&\phantom{8}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{120}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Brown}{1}& 0 \downarrow&5&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$120$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-120 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Crimson}{0}&\phantom{0}&\phantom{8}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{120}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0& 5 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$120$$$'s are in $$$105$$$?

The answer is $$$0$$$.

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

Now, $$$105-120 \cdot 0 = 105 - 0= 105$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Red}{0}&\phantom{8}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{120}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&5& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Red}{1}&\color{Red}{0}&\color{Red}{5}&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&0&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$120$$$'s are in $$$1050$$$?

The answer is $$$8$$$.

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

Now, $$$1050-120 \cdot 8 = 1050 - 960= 90$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{GoldenRod}{8}&\phantom{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{120}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&5&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&5&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{1}&\color{GoldenRod}{0}&\color{GoldenRod}{5}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&0&\phantom{.}\\\hline\phantom{lll}&&9&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$120$$$'s are in $$$900$$$?

The answer is $$$7$$$.

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

Now, $$$900-120 \cdot 7 = 900 - 840= 60$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&\color{BlueViolet}{7}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{120}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&5&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&5&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&0&5&0&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&0&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{9}&\color{BlueViolet}{0}&\color{BlueViolet}{0}&\phantom{.}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&8&4&0&\phantom{.}\\\hline\phantom{lll}&&&6&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$120$$$'s are in $$$600$$$?

The answer is $$$5$$$.

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

Now, $$$600-120 \cdot 5 = 600 - 600= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&7&.&\color{Chocolate}{5}\end{array}&\\\color{Magenta}{120}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&5&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&5&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&0&5&0&\phantom{.}\\-&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&0&\phantom{.}\\\hline\phantom{lll}&&9&0&0&\phantom{.}\\&-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&8&4&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Chocolate}{6}&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{0}\\&&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&6&0&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{10500}{120}=87.5 \overline{}$$$

Answer: $$$\frac{10500}{120}=87.5\overline{}$$$