分数转小数计算器

Your input: convert $$$\frac{900}{36}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\36&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$36$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-36 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Peru}{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Peru}{9}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$36$$$'s are in $$$90$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$90-36 \cdot 2 = 90 - 72= 18$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{BlueViolet}{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{9}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}7&2&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$36$$$'s are in $$$180$$$?

The answer is $$$5$$$.

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

Now, $$$180-36 \cdot 5 = 180 - 180= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&2&\color{SaddleBrown}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}7&2&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{8}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$36$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-36 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&2&5&.&\color{Green}{0}\end{array}&\\\color{Magenta}{36}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}7&2&\phantom{.}\\\hline\phantom{lll}1&8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&&\color{Green}{0}&\phantom{.}&\color{Green}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{900}{36}=25.0 \overline{}$$$

Answer: $$$\frac{900}{36}=25.0\overline{}$$$