분수를 소수로 변환하는 계산기

Your input: convert $$$\frac{1600}{18}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{8}&\phantom{.}&\phantom{8}&\phantom{8}&\phantom{8}\end{array}&\\18&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&6&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$18$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-18 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Crimson}{0}&\phantom{0}&\phantom{8}&\phantom{8}&\phantom{.}&\phantom{8}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Crimson}{1}& 6 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$18$$$'s are in $$$16$$$?

The answer is $$$0$$$.

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

Now, $$$16-18 \cdot 0 = 16 - 0= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{DarkBlue}{0}&\phantom{8}&\phantom{8}&\phantom{.}&\phantom{8}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&6& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{6}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$18$$$'s are in $$$160$$$?

The answer is $$$8$$$.

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

Now, $$$160-18 \cdot 8 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{SaddleBrown}{8}&\phantom{8}&\phantom{.}&\phantom{8}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&6&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{6}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$18$$$'s are in $$$160$$$?

The answer is $$$8$$$.

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

Now, $$$160-18 \cdot 8 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&\color{Chocolate}{8}&\phantom{.}&\phantom{8}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&6&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{1}&\color{Chocolate}{6}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$18$$$'s are in $$$160$$$?

The answer is $$$8$$$.

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

Now, $$$160-18 \cdot 8 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&8&.&\color{Blue}{8}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&6&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&4&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{1}&\color{Blue}{6}&\phantom{.}&\color{Blue}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$18$$$'s are in $$$160$$$?

The answer is $$$8$$$.

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

Now, $$$160-18 \cdot 8 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&8&.&8&\color{DeepPink}{8}&\phantom{8}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&6&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&\color{DeepPink}{1}&\phantom{.}&\color{DeepPink}{6}&\color{DeepPink}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$18$$$'s are in $$$160$$$?

The answer is $$$8$$$.

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

Now, $$$160-18 \cdot 8 = 160 - 144= 16$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&8&.&8&8&\color{Green}{8}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&6&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&4&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&\color{Green}{1}&\color{Green}{6}&\color{Green}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&1&6\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1600}{18}=88.8 \overline{8}$$$

Answer: $$$\frac{1600}{18}=88.8\overline{8}$$$