分数转小数计算器

Your input: convert $$$\frac{1700}{33}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{5}&\phantom{1}&\phantom{.}&\phantom{5}&\phantom{1}&\phantom{5}&\phantom{1}\end{array}&\\33&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&7&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$33$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-33 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{Chartreuse}{0}&\phantom{0}&\phantom{5}&\phantom{1}&\phantom{.}&\phantom{5}&\phantom{1}&\phantom{5}&\phantom{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{Chartreuse}{1}& 7 \downarrow&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$33$$$'s are in $$$17$$$?

The answer is $$$0$$$.

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

Now, $$$17-33 \cdot 0 = 17 - 0= 17$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{Green}{0}&\phantom{5}&\phantom{1}&\phantom{.}&\phantom{5}&\phantom{1}&\phantom{5}&\phantom{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&7& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{7}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$33$$$'s are in $$$170$$$?

The answer is $$$5$$$.

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

Now, $$$170-33 \cdot 5 = 170 - 165= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&\color{Purple}{5}&\phantom{1}&\phantom{.}&\phantom{5}&\phantom{1}&\phantom{5}&\phantom{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&7&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{7}&\color{Purple}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$33$$$'s are in $$$50$$$?

The answer is $$$1$$$.

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

Now, $$$50-33 \cdot 1 = 50 - 33= 17$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&5&\color{Violet}{1}&\phantom{.}&\phantom{5}&\phantom{1}&\phantom{5}&\phantom{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&7&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&5&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{5}&\color{Violet}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&3&\phantom{.}\\\hline\phantom{lll}&&1&7&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$33$$$'s are in $$$170$$$?

The answer is $$$5$$$.

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

Now, $$$170-33 \cdot 5 = 170 - 165= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&5&1&.&\color{Brown}{5}&\phantom{1}&\phantom{5}&\phantom{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&7&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&3&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{1}&\color{Brown}{7}&\phantom{.}&\color{Brown}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&6&\phantom{.}&5\\\hline\phantom{lll}&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$33$$$'s are in $$$50$$$?

The answer is $$$1$$$.

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

Now, $$$50-33 \cdot 1 = 50 - 33= 17$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&5&1&.&5&\color{Blue}{1}&\phantom{5}&\phantom{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&7&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&3&\phantom{.}\\\hline\phantom{lll}&&1&7&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&6&\phantom{.}&5\\\hline\phantom{lll}&&&&&\color{Blue}{5}&\color{Blue}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&3\\\hline\phantom{lll}&&&&&1&7&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$33$$$'s are in $$$170$$$?

The answer is $$$5$$$.

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

Now, $$$170-33 \cdot 5 = 170 - 165= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&5&1&.&5&1&\color{Peru}{5}&\phantom{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&7&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&3&\phantom{.}\\\hline\phantom{lll}&&1&7&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&6&\phantom{.}&5\\\hline\phantom{lll}&&&&&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&3\\\hline\phantom{lll}&&&&&\color{Peru}{1}&\color{Peru}{7}&\color{Peru}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&6&5\\\hline\phantom{lll}&&&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$33$$$'s are in $$$50$$$?

The answer is $$$1$$$.

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

Now, $$$50-33 \cdot 1 = 50 - 33= 17$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&0&5&1&.&5&1&5&\color{Fuchsia}{1}\end{array}&\\\color{Magenta}{33}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}1&7&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&3&\phantom{.}\\\hline\phantom{lll}&&1&7&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&6&\phantom{.}&5\\\hline\phantom{lll}&&&&&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&3\\\hline\phantom{lll}&&&&&1&7&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&6&5\\\hline\phantom{lll}&&&&&&&\color{Fuchsia}{5}&\color{Fuchsia}{0}\\&&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&3\\\hline\phantom{lll}&&&&&&&1&7\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1700}{33}=51. \overline{51}$$$

Answer: $$$\frac{1700}{33}=51.\overline{51}$$$