분수를 소수로 변환하는 계산기

Your input: convert $$$\frac{2400}{36}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\36&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}2&4&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$36$$$'s are in $$$2$$$?

The answer is $$$0$$$.

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

Now, $$$2-36 \cdot 0 = 2 - 0= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{Blue}{0}&\phantom{0}&\phantom{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{Blue}{2}& 4 \downarrow&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&4&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$36$$$'s are in $$$24$$$?

The answer is $$$0$$$.

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

Now, $$$24-36 \cdot 0 = 24 - 0= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{Green}{0}&\phantom{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}2&4& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{2}&\color{Green}{4}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$36$$$'s are in $$$240$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$240-36 \cdot 6 = 240 - 216= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&\color{Purple}{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}2&4&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{2}&\color{Purple}{4}&\color{Purple}{0}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&1&6&\phantom{.}\\\hline\phantom{lll}&2&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$36$$$'s are in $$$240$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$240-36 \cdot 6 = 240 - 216= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&6&\color{Brown}{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}2&4&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&1&6&\phantom{.}\\\hline\phantom{lll}&\color{Brown}{2}&\color{Brown}{4}&\color{Brown}{0}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&6&\phantom{.}\\\hline\phantom{lll}&&2&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$36$$$'s are in $$$240$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$240-36 \cdot 6 = 240 - 216= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&6&6&.&\color{DarkMagenta}{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}2&4&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&1&6&\phantom{.}\\\hline\phantom{lll}&2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&6&\phantom{.}\\\hline\phantom{lll}&&\color{DarkMagenta}{2}&\color{DarkMagenta}{4}&\phantom{.}&\color{DarkMagenta}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&2&\phantom{.}&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$36$$$'s are in $$$240$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$240-36 \cdot 6 = 240 - 216= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&6&6&.&6&\color{Chocolate}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}2&4&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&1&6&\phantom{.}\\\hline\phantom{lll}&2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&6&\phantom{.}\\\hline\phantom{lll}&&2&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&\color{Chocolate}{2}&\phantom{.}&\color{Chocolate}{4}&\color{Chocolate}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&1&6\\\hline\phantom{lll}&&&&&2&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$36$$$'s are in $$$240$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$240-36 \cdot 6 = 240 - 216= 24$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&6&6&.&6&6&\color{Violet}{6}&\phantom{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}2&4&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&1&6&\phantom{.}\\\hline\phantom{lll}&2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&6&\phantom{.}\\\hline\phantom{lll}&&2&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&2&\phantom{.}&4&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&1&6\\\hline\phantom{lll}&&&&&\color{Violet}{2}&\color{Violet}{4}&\color{Violet}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&1&6\\\hline\phantom{lll}&&&&&&2&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$36$$$'s are in $$$240$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$240-36 \cdot 6 = 240 - 216= 24$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&6&6&.&6&6&6&\color{Red}{6}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}2&4&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}2&1&6&\phantom{.}\\\hline\phantom{lll}&2&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&1&6&\phantom{.}\\\hline\phantom{lll}&&2&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&1&\phantom{.}&6\\\hline\phantom{lll}&&&2&\phantom{.}&4&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&1&6\\\hline\phantom{lll}&&&&&2&4&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&1&6\\\hline\phantom{lll}&&&&&&\color{Red}{2}&\color{Red}{4}&\color{Red}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&2&1&6\\\hline\phantom{lll}&&&&&&&2&4\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{2400}{36}=66.66 \overline{6}$$$

Answer: $$$\frac{2400}{36}=66.66\overline{6}$$$