分数を小数に変換する電卓
分数を小数に手順を追って変換
この電卓は、与えられた分数（真分数または仮分数）または帯分数を、小数（循環小数となる場合もあります）に変換し、計算手順を表示します。
Solution
Your input: convert $$$\frac{900}{30}$$$ into a decimal.
Write the problem in the special format:
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 1
How many $$$30$$$'s are in $$$9$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$9-30 \cdot 0 = 9 - 0= 9$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{SaddleBrown}{0}&\phantom{3}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{SaddleBrown}{9}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 2
How many $$$30$$$'s are in $$$90$$$?
The answer is $$$3$$$.
Write down $$$3$$$ in the upper part of the table.
Now, $$$90-30 \cdot 3 = 90 - 90= 0$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{GoldenRod}{3}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{9}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 3
How many $$$30$$$'s are in $$$0$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$0-30 \cdot 0 = 0 - 0= 0$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&3&\color{Green}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&\phantom{.}\\\hline\phantom{lll}&\color{Green}{0}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 4
How many $$$30$$$'s are in $$$0$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$0-30 \cdot 0 = 0 - 0= 0$$$.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&3&0&.&\color{BlueViolet}{0}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{0}&\phantom{.}&\color{BlueViolet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{900}{30}=30. \overline{0}$$$
Answer: $$$\frac{900}{30}=30.\overline{0}$$$