Fraction to Decimal Calculator

Your input: convert $\frac{200}{30}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}2&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $30$'s are in $2$? The answer is $0$.

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

Now, $2-0 \cdot 30 = 2 - 0= 2$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Purple}{0}&\phantom{0}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Purple}{2}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $30$'s are in $20$? The answer is $0$.

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

Now, $20-0 \cdot 30 = 20 - 0= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DarkBlue}{0}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{2}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $30$'s are in $200$? The answer is $6$.

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

Now, $200-6 \cdot 30 = 200 - 180= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{BlueViolet}{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{2}&\color{BlueViolet}{0}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $30$'s are in $200$? The answer is $6$.

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

Now, $200-6 \cdot 30 = 200 - 180= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&.&\color{OrangeRed}{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&\color{OrangeRed}{2}&\color{OrangeRed}{0}&\phantom{.}&\color{OrangeRed}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&0\\\hline\phantom{lll}&&2&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $30$'s are in $200$? The answer is $6$.

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

Now, $200-6 \cdot 30 = 200 - 180= 20$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&.&6&\color{GoldenRod}{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}2&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&0\\\hline\phantom{lll}&&\color{GoldenRod}{2}&\phantom{.}&\color{GoldenRod}{0}&\color{GoldenRod}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{200}{30}=6. \overline{6}$

Answer: $\frac{200}{30}=6.\overline{6}$