分數轉小數計算器

Your input: convert $$$\frac{100}{12}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\12&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$12$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-12 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Fuchsia}{1}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$12$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-12 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Chocolate}{0}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$12$$$'s are in $$$100$$$?

The answer is $$$8$$$.

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

Now, $$$100-12 \cdot 8 = 100 - 96= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{Purple}{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{0}&\color{Purple}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

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

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&.&\color{OrangeRed}{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&\color{OrangeRed}{4}&\phantom{.}&\color{OrangeRed}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

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

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&.&3&\color{DarkMagenta}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&\color{DarkMagenta}{4}&\color{DarkMagenta}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&6\\\hline\phantom{lll}&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

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

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&.&3&3&\color{Blue}{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&6\\\hline\phantom{lll}&&&&&\color{Blue}{4}&\color{Blue}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&6\\\hline\phantom{lll}&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

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

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&.&3&3&3&\color{GoldenRod}{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&6\\\hline\phantom{lll}&&&&&4&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&6\\\hline\phantom{lll}&&&&&&\color{GoldenRod}{4}&\color{GoldenRod}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&3&6\\\hline\phantom{lll}&&&&&&&4\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{100}{12}=8.33 \overline{3}$$$

Answer: $$$\frac{100}{12}=8.33\overline{3}$$$