分数转小数计算器

Your input: convert $$$\frac{400}{3}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\3&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$3$$$'s are in $$$4$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$4-3 \cdot 1 = 4 - 3= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Chartreuse}{1}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Chartreuse}{4}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}1&\color{Green}{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}1&3&\color{Purple}{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{1}&\color{Purple}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}1&3&3&.&\color{Violet}{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{1}&\phantom{.}&\color{Violet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9\\\hline\phantom{lll}&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}1&3&3&.&3&\color{Brown}{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&\phantom{.}\\\hline\phantom{lll}&&1&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&9\\\hline\phantom{lll}&&&&\color{Brown}{1}&\color{Brown}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&9\\\hline\phantom{lll}&&&&&1\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{400}{3}=133. \overline{3}$$$

Answer: $$$\frac{400}{3}=133.\overline{3}$$$