分數轉小數計算器

Your input: convert $$$\frac{200}{6}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\6&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}2&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$6$$$'s are in $$$2$$$?

The answer is $$$0$$$.

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

Now, $$$2-6 \cdot 0 = 2 - 0= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{DarkMagenta}{0}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{DarkMagenta}{2}& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$6$$$'s are in $$$20$$$?

The answer is $$$3$$$.

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

Now, $$$20-6 \cdot 3 = 20 - 18= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{OrangeRed}{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{2}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$6$$$'s are in $$$20$$$?

The answer is $$$3$$$.

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

Now, $$$20-6 \cdot 3 = 20 - 18= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&3&\color{DarkCyan}{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&8&\phantom{.}\\\hline\phantom{lll}&\color{DarkCyan}{2}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}\\\hline\phantom{lll}&&2&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$6$$$'s are in $$$20$$$?

The answer is $$$3$$$.

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

Now, $$$20-6 \cdot 3 = 20 - 18= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&3&3&.&\color{GoldenRod}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}\\\hline\phantom{lll}&&\color{GoldenRod}{2}&\phantom{.}&\color{GoldenRod}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$6$$$'s are in $$$20$$$?

The answer is $$$3$$$.

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

Now, $$$20-6 \cdot 3 = 20 - 18= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&3&3&.&3&\color{Violet}{3}&\phantom{3}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}\\\hline\phantom{lll}&&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&8\\\hline\phantom{lll}&&&&\color{Violet}{2}&\color{Violet}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&8\\\hline\phantom{lll}&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$6$$$'s are in $$$20$$$?

The answer is $$$3$$$.

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

Now, $$$20-6 \cdot 3 = 20 - 18= 2$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&3&3&.&3&3&\color{Green}{3}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}2&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}\\\hline\phantom{lll}&&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&8\\\hline\phantom{lll}&&&&&\color{Green}{2}&\color{Green}{0}\\&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8\\\hline\phantom{lll}&&&&&&2\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{200}{6}=33.3 \overline{3}$$$

Answer: $$$\frac{200}{6}=33.3\overline{3}$$$