분수를 소수로 변환하는 계산기

Your input: convert $$$\frac{15000}{200}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\200&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&5&0&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$200$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-200 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Peru}{0}&\phantom{0}&\phantom{0}&\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Peru}{1}& 5 \downarrow&0&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$200$$$'s are in $$$15$$$?

The answer is $$$0$$$.

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

Now, $$$15-200 \cdot 0 = 15 - 0= 15$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{BlueViolet}{0}&\phantom{0}&\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5& 0 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{1}&\color{BlueViolet}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$200$$$'s are in $$$150$$$?

The answer is $$$0$$$.

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

Now, $$$150-200 \cdot 0 = 150 - 0= 150$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{SaddleBrown}{0}&\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{5}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&5&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$200$$$'s are in $$$1500$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$1500-200 \cdot 7 = 1500 - 1400= 100$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Green}{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{5}&\color{Green}{0}&\color{Green}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$200$$$'s are in $$$1000$$$?

The answer is $$$5$$$.

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

Now, $$$1000-200 \cdot 5 = 1000 - 1000= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&7&\color{DarkBlue}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&5&0&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkBlue}{1}&\color{DarkBlue}{0}&\color{DarkBlue}{0}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&0&0&0&\phantom{.}\\\hline\phantom{lll}&&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$200$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-200 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&7&5&.&\color{DarkCyan}{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&5&0&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&5&0&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&0&0&0&\phantom{.}\\\hline\phantom{lll}&&&&\color{DarkCyan}{0}&\phantom{.}&\color{DarkCyan}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Since the remainder is $$$0$$$, then we are done.

Therefore, $$$\frac{15000}{200}=75.0$$$

Answer: $$$\frac{15000}{200}=75.0$$$