分数转小数计算器

Your input: convert $$$\frac{14100}{150}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{9}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\150&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&4&1&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Chartreuse}{0}&\phantom{0}&\phantom{0}&\phantom{9}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Chartreuse}{1}& 4 \downarrow&1&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$150$$$'s are in $$$14$$$?

The answer is $$$0$$$.

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

Now, $$$14-150 \cdot 0 = 14 - 0= 14$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Green}{0}&\phantom{0}&\phantom{9}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4& 1 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{4}&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$150$$$'s are in $$$141$$$?

The answer is $$$0$$$.

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

Now, $$$141-150 \cdot 0 = 141 - 0= 141$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Purple}{0}&\phantom{9}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&1& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{4}&\color{Purple}{1}&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&4&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$150$$$'s are in $$$1410$$$?

The answer is $$$9$$$.

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

Now, $$$1410-150 \cdot 9 = 1410 - 1350= 60$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Violet}{9}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&1&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&1&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{1}&\color{Violet}{4}&\color{Violet}{1}&\color{Violet}{0}&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&3&5&0&\phantom{.}\\\hline\phantom{lll}&&6&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&9&\color{Brown}{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&1&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&1&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&4&1&0&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&3&5&0&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{6}&\color{Brown}{0}&\color{Brown}{0}&\phantom{.}\\&-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&6&0&0&\phantom{.}\\\hline\phantom{lll}&&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

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

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&9&4&.&\color{Blue}{0}\end{array}&\\\color{Magenta}{150}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&4&1&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&1&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&4&1&0&\phantom{.}\\-&\phantom{4}&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&3&5&0&\phantom{.}\\\hline\phantom{lll}&&6&0&0&\phantom{.}\\&-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&6&0&0&\phantom{.}\\\hline\phantom{lll}&&&&\color{Blue}{0}&\phantom{.}&\color{Blue}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{14100}{150}=94.0 \overline{}$$$

Answer: $$$\frac{14100}{150}=94.0\overline{}$$$