Fraction to Decimal Calculator

Your input: convert $$$\frac{300}{6}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\6&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}3&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$6$$$'s are in $$$3$$$?

The answer is $$$0$$$.

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

Now, $$$3-6 \cdot 0 = 3 - 0= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Fuchsia}{0}&\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Fuchsia}{3}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$6$$$'s are in $$$30$$$?

The answer is $$$5$$$.

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

Now, $$$30-6 \cdot 5 = 30 - 30= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{Peru}{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}3&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{3}&\color{Peru}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$6$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-6 \cdot 0 = 0 - 0= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&5&\color{DeepPink}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}3&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&0&\phantom{.}\\\hline\phantom{lll}&\color{DeepPink}{0}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$6$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-6 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&5&0&.&\color{Chocolate}{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}3&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{300}{6}=50.0 \overline{}$$$

Answer: $$$\frac{300}{6}=50.0\overline{}$$$