분수를 소수로 변환하는 계산기

Your input: convert $$$\frac{1500}{18}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\18&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Crimson}{0}&\phantom{0}&\phantom{8}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Crimson}{1}& 5 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$18$$$'s are in $$$15$$$?

The answer is $$$0$$$.

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

Now, $$$15-18 \cdot 0 = 15 - 0= 15$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{DarkBlue}{0}&\phantom{8}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&5& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$18$$$'s are in $$$150$$$?

The answer is $$$8$$$.

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

Now, $$$150-18 \cdot 8 = 150 - 144= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{SaddleBrown}{8}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&5&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{5}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$18$$$'s are in $$$60$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$60-18 \cdot 3 = 60 - 54= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&\color{Chocolate}{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&5&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&\color{Chocolate}{6}&\color{Chocolate}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&4&\phantom{.}\\\hline\phantom{lll}&&&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$18$$$'s are in $$$60$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$60-18 \cdot 3 = 60 - 54= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&3&.&\color{Blue}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&5&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&4&\phantom{.}\\\hline\phantom{lll}&&&\color{Blue}{6}&\phantom{.}&\color{Blue}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$18$$$'s are in $$$60$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$60-18 \cdot 3 = 60 - 54= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&3&.&3&\color{DeepPink}{3}&\phantom{3}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&5&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&4&\phantom{.}\\\hline\phantom{lll}&&&6&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&\color{DeepPink}{6}&\color{DeepPink}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&5&4\\\hline\phantom{lll}&&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$18$$$'s are in $$$60$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$60-18 \cdot 3 = 60 - 54= 6$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&3&.&3&3&\color{Green}{3}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&5&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&4&\phantom{.}\\\hline\phantom{lll}&&&6&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&5&4\\\hline\phantom{lll}&&&&&&\color{Green}{6}&\color{Green}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&4\\\hline\phantom{lll}&&&&&&&6\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1500}{18}=83.3 \overline{3}$$$

Answer: $$$\frac{1500}{18}=83.3\overline{3}$$$