分数を小数に変換する電卓

Your input: convert $$$\frac{300}{3}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\3&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}3&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$3$$$'s are in $$$3$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$3-3 \cdot 1 = 3 - 3= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Brown}{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Brown}{3}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$3$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-3 \cdot 0 = 0 - 0= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}1&\color{DarkMagenta}{0}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}3&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{0}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$3$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-3 \cdot 0 = 0 - 0= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}1&0&\color{DarkBlue}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}3&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkBlue}{0}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$3$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-3 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}1&0&0&.&\color{Purple}{0}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}3&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{0}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{300}{3}=100. \overline{0}$$$

Answer: $$$\frac{300}{3}=100.\overline{0}$$$