分数转小数计算器

Your input: convert $$$\frac{9900}{150}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{6}&\phantom{.}&\phantom{0}\end{array}&\\150&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}9&9&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$150$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-150 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Peru}{0}&\phantom{0}&\phantom{6}&\phantom{6}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Peru}{9}& 9 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&9&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$150$$$'s are in $$$99$$$?

The answer is $$$0$$$.

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

Now, $$$99-150 \cdot 0 = 99 - 0= 99$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Brown}{0}&\phantom{6}&\phantom{6}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&9& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{9}&\color{Brown}{9}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}9&9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$150$$$'s are in $$$990$$$?

The answer is $$$6$$$.

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

Now, $$$990-150 \cdot 6 = 990 - 900= 90$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{DarkMagenta}{6}&\phantom{6}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&9&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{9}&\color{DarkMagenta}{9}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&0&\phantom{.}\\\hline\phantom{lll}&9&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$150$$$'s are in $$$900$$$?

The answer is $$$6$$$.

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

Now, $$$900-150 \cdot 6 = 900 - 900= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{DarkBlue}{6}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&9&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}9&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkBlue}{9}&\color{DarkBlue}{0}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$150$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-150 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&6&.&\color{Purple}{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}9&9&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}9&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&0&\phantom{.}\\\hline\phantom{lll}&9&0&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Purple}{0}&\phantom{.}&\color{Purple}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{9900}{150}=66.0 \overline{}$$$

Answer: $$$\frac{9900}{150}=66.0\overline{}$$$