分数を小数に変換する電卓

Your input: convert $$$\frac{1600}{30}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{5}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&6&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$30$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-30 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Peru}{0}&\phantom{0}&\phantom{5}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Peru}{1}& 6 \downarrow&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$30$$$'s are in $$$16$$$?

The answer is $$$0$$$.

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

Now, $$$16-30 \cdot 0 = 16 - 0= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{DarkCyan}{0}&\phantom{5}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{1}&\color{DarkCyan}{6}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$30$$$'s are in $$$160$$$?

The answer is $$$5$$$.

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

Now, $$$160-30 \cdot 5 = 160 - 150= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Chocolate}{5}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{6}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&5&\color{Fuchsia}{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&5&0&\phantom{.}\\\hline\phantom{lll}&\color{Fuchsia}{1}&\color{Fuchsia}{0}&\color{Fuchsia}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&5&3&.&\color{DeepPink}{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&\phantom{.}\\\hline\phantom{lll}&&\color{DeepPink}{1}&\color{DeepPink}{0}&\phantom{.}&\color{DeepPink}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0\\\hline\phantom{lll}&&&1&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&5&3&.&3&\color{GoldenRod}{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&0&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9&0\\\hline\phantom{lll}&&&\color{GoldenRod}{1}&\phantom{.}&\color{GoldenRod}{0}&\color{GoldenRod}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&9&\phantom{.}&0\\\hline\phantom{lll}&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1600}{30}=53. \overline{3}$$$

Answer: $$$\frac{1600}{30}=53.\overline{3}$$$