分数转小数计算器

Your input: convert $$$\frac{500}{11}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\11&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}5&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$11$$$'s are in $$$5$$$?

The answer is $$$0$$$.

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

Now, $$$5-11 \cdot 0 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{DarkCyan}{0}&\phantom{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{DarkCyan}{5}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$11$$$'s are in $$$50$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$50-11 \cdot 4 = 50 - 44= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{OrangeRed}{4}&\phantom{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{5}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$11$$$'s are in $$$60$$$?

The answer is $$$5$$$.

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

Now, $$$60-11 \cdot 5 = 60 - 55= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&\color{Purple}{5}&\phantom{.}&\phantom{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{6}&\color{Purple}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$11$$$'s are in $$$50$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$50-11 \cdot 4 = 50 - 44= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&\color{Brown}{4}&\phantom{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{5}&\phantom{.}&\color{Brown}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$11$$$'s are in $$$60$$$?

The answer is $$$5$$$.

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

Now, $$$60-11 \cdot 5 = 60 - 55= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&4&\color{DeepPink}{5}&\phantom{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&\color{DeepPink}{6}&\color{DeepPink}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&5\\\hline\phantom{lll}&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$11$$$'s are in $$$50$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$50-11 \cdot 4 = 50 - 44= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&4&5&\color{Peru}{4}&\phantom{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&5\\\hline\phantom{lll}&&&&&\color{Peru}{5}&\color{Peru}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$11$$$'s are in $$$60$$$?

The answer is $$$5$$$.

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

Now, $$$60-11 \cdot 5 = 60 - 55= 5$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&4&5&.&4&5&4&\color{Chocolate}{5}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&5&\phantom{.}\\\hline\phantom{lll}&&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&5\\\hline\phantom{lll}&&&&&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&&\color{Chocolate}{6}&\color{Chocolate}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&5&5\\\hline\phantom{lll}&&&&&&&5\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{500}{11}=45. \overline{45}$$$

Answer: $$$\frac{500}{11}=45.\overline{45}$$$