Fraction to Decimal Calculator

Your input: convert $$$\frac{1200}{48}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\48&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$48$$$'s are in $$$1$$$? The answer is $$$0$$$.

Write down the calculated result in the upper part of the table.

Now, $$$1-0 \cdot 48 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Chocolate}{0}&\phantom{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Chocolate}{1}& 2 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$48$$$'s are in $$$12$$$? The answer is $$$0$$$.

Write down the calculated result in the upper part of the table.

Now, $$$12-0 \cdot 48 = 12 - 0= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{SaddleBrown}{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$48$$$'s are in $$$120$$$? The answer is $$$2$$$.

Write down the calculated result in the upper part of the table.

Now, $$$120-2 \cdot 48 = 120 - 96= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{OrangeRed}{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{1}&\color{OrangeRed}{2}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&2&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$48$$$'s are in $$$240$$$? The answer is $$$5$$$.

Write down the calculated result in the upper part of the table.

Now, $$$240-5 \cdot 48 = 240 - 240= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&\color{Chartreuse}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&\color{Chartreuse}{2}&\color{Chartreuse}{4}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&4&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$48$$$'s are in $$$0$$$? The answer is $$$0$$$.

Write down the calculated result in the upper part of the table.

Now, $$$0-0 \cdot 48 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&5&.&\color{DarkCyan}{0}\end{array}&\\\color{Magenta}{48}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&2&4&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&4&0&\phantom{.}\\\hline\phantom{lll}&&&\color{DarkCyan}{0}&\phantom{.}&\color{DarkCyan}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1200}{48}=25.0 \overline{}$$$

Answer: $$$\frac{1200}{48}=25.0\overline{}$$$