分数转小数计算器

Your input: convert $$$\frac{1700}{18}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{9}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\18&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&7&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$18$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-18 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Green}{0}&\phantom{0}&\phantom{9}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Green}{1}& 7 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$18$$$'s are in $$$17$$$?

The answer is $$$0$$$.

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

Now, $$$17-18 \cdot 0 = 17 - 0= 17$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Peru}{0}&\phantom{9}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{1}&\color{Peru}{7}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$18$$$'s are in $$$170$$$?

The answer is $$$9$$$.

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

Now, $$$170-18 \cdot 9 = 170 - 162= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{DarkBlue}{9}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{7}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&2&\phantom{.}\\\hline\phantom{lll}&&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$18$$$'s are in $$$80$$$?

The answer is $$$4$$$.

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

Now, $$$80-18 \cdot 4 = 80 - 72= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&9&\color{SaddleBrown}{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&2&\phantom{.}\\\hline\phantom{lll}&&\color{SaddleBrown}{8}&\color{SaddleBrown}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&2&\phantom{.}\\\hline\phantom{lll}&&&8&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$18$$$'s are in $$$80$$$?

The answer is $$$4$$$.

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

Now, $$$80-18 \cdot 4 = 80 - 72= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&9&4&.&\color{Crimson}{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&2&\phantom{.}\\\hline\phantom{lll}&&8&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&2&\phantom{.}\\\hline\phantom{lll}&&&\color{Crimson}{8}&\phantom{.}&\color{Crimson}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$18$$$'s are in $$$80$$$?

The answer is $$$4$$$.

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

Now, $$$80-18 \cdot 4 = 80 - 72= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&9&4&.&4&\color{Violet}{4}&\phantom{4}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&2&\phantom{.}\\\hline\phantom{lll}&&8&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&2&\phantom{.}\\\hline\phantom{lll}&&&8&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&&\color{Violet}{8}&\color{Violet}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&7&2\\\hline\phantom{lll}&&&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$18$$$'s are in $$$80$$$?

The answer is $$$4$$$.

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

Now, $$$80-18 \cdot 4 = 80 - 72= 8$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&9&4&.&4&4&\color{Red}{4}\end{array}&\\\color{Magenta}{18}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&7&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&6&2&\phantom{.}\\\hline\phantom{lll}&&8&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&2&\phantom{.}\\\hline\phantom{lll}&&&8&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&&8&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&7&2\\\hline\phantom{lll}&&&&&&\color{Red}{8}&\color{Red}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&7&2\\\hline\phantom{lll}&&&&&&&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1700}{18}=94.4 \overline{4}$$$

Answer: $$$\frac{1700}{18}=94.4\overline{4}$$$