分数转小数计算器

Your input: convert $$$\frac{12600}{150}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\150&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&2&6&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$150$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-150 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Crimson}{0}&\phantom{0}&\phantom{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Crimson}{1}& 2 \downarrow&6&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$150$$$'s are in $$$12$$$?

The answer is $$$0$$$.

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

Now, $$$12-150 \cdot 0 = 12 - 0= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{DarkBlue}{0}&\phantom{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2& 6 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{2}&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$150$$$'s are in $$$126$$$?

The answer is $$$0$$$.

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

Now, $$$126-150 \cdot 0 = 126 - 0= 126$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{SaddleBrown}{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&6& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{2}&\color{SaddleBrown}{6}&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$150$$$'s are in $$$1260$$$?

The answer is $$$8$$$.

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

Now, $$$1260-150 \cdot 8 = 1260 - 1200= 60$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Chocolate}{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&6&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&6&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{2}&\color{Chocolate}{6}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&6&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$150$$$'s are in $$$600$$$?

The answer is $$$4$$$.

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

Now, $$$600-150 \cdot 4 = 600 - 600= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&\color{Blue}{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&6&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&6&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&6&0&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{6}&\color{Blue}{0}&\color{Blue}{0}&\phantom{.}\\&-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&6&0&0&\phantom{.}\\\hline\phantom{lll}&&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

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

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&4&.&\color{DeepPink}{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&6&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&6&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&6&0&\phantom{.}\\-&\phantom{2}&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&6&0&0&\phantom{.}\\&-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&6&0&0&\phantom{.}\\\hline\phantom{lll}&&&&\color{DeepPink}{0}&\phantom{.}&\color{DeepPink}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{12600}{150}=84.0 \overline{}$$$

Answer: $$$\frac{12600}{150}=84.0\overline{}$$$