分數轉小數計算器

Your input: convert $$$\frac{1100}{12}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{9}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\12&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&1&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{Crimson}{0}&\phantom{0}&\phantom{9}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{Crimson}{1}& 1 \downarrow&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$12$$$'s are in $$$11$$$?

The answer is $$$0$$$.

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

Now, $$$11-12 \cdot 0 = 11 - 0= 11$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{DarkBlue}{0}&\phantom{9}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{1}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$12$$$'s are in $$$110$$$?

The answer is $$$9$$$.

Write down $$$9$$$ in the upper part of the table.

Now, $$$110-12 \cdot 9 = 110 - 108= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&\color{Green}{9}&\phantom{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{1}&\color{Green}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$12$$$'s are in $$$20$$$?

The answer is $$$1$$$.

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

Now, $$$20-12 \cdot 1 = 20 - 12= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&9&\color{Chartreuse}{1}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&&\color{Chartreuse}{2}&\color{Chartreuse}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&2&\phantom{.}\\\hline\phantom{lll}&&&8&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$12$$$'s are in $$$80$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$80-12 \cdot 6 = 80 - 72= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&9&1&.&\color{Peru}{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&2&\phantom{.}\\\hline\phantom{lll}&&&\color{Peru}{8}&\phantom{.}&\color{Peru}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$12$$$'s are in $$$80$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$80-12 \cdot 6 = 80 - 72= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&9&1&.&6&\color{Red}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&2&\phantom{.}\\\hline\phantom{lll}&&&8&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&&\color{Red}{8}&\color{Red}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&7&2\\\hline\phantom{lll}&&&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$12$$$'s are in $$$80$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$80-12 \cdot 6 = 80 - 72= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&9&1&.&6&6&\color{Chocolate}{6}&\phantom{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&2&\phantom{.}\\\hline\phantom{lll}&&&8&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&&8&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&7&2\\\hline\phantom{lll}&&&&&&\color{Chocolate}{8}&\color{Chocolate}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&7&2\\\hline\phantom{lll}&&&&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$12$$$'s are in $$$80$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$80-12 \cdot 6 = 80 - 72= 8$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&9&1&.&6&6&6&\color{BlueViolet}{6}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&1&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&8&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&2&\phantom{.}\\\hline\phantom{lll}&&&8&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&&8&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&7&2\\\hline\phantom{lll}&&&&&&8&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&7&2\\\hline\phantom{lll}&&&&&&&\color{BlueViolet}{8}&\color{BlueViolet}{0}\\&&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&2\\\hline\phantom{lll}&&&&&&&&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1100}{12}=91.66 \overline{6}$$$

Answer: $$$\frac{1100}{12}=91.66\overline{6}$$$