分数转小数计算器

逐步将分数转换为小数

该计算器会将给定的分数(真分数或假分数)或带分数转换为小数(可能为循环小数),并显示步骤。

Enter a fraction or

If you don't need a mixed number, leave the left cell empty.
If you need a negative fraction, write the minus sign in the left cell.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: convert $$$\frac{1000}{27}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{3}&\phantom{7}&\phantom{.}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\27&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&0&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$27$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-27 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}\color{DeepPink}{0}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{.}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}\color{DeepPink}{1}& 0 \downarrow&0&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$27$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-27 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&\color{Fuchsia}{0}&\phantom{3}&\phantom{7}&\phantom{.}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0& 0 \downarrow&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Fuchsia}{1}&\color{Fuchsia}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$27$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-27 \cdot 3 = 100 - 81= 19$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&\color{Crimson}{3}&\phantom{7}&\phantom{.}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0& 0 \downarrow&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{0}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$27$$$'s are in $$$190$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$190-27 \cdot 7 = 190 - 189= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&3&\color{BlueViolet}{7}&\phantom{.}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0&0&.& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&\color{BlueViolet}{1}&\color{BlueViolet}{9}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$27$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-27 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&3&7&.&\color{DarkMagenta}{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0&0&.&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&9&\phantom{.}\\\hline\phantom{lll}&&&\color{DarkMagenta}{1}&\phantom{.}&\color{DarkMagenta}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&1&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$27$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-27 \cdot 3 = 100 - 81= 19$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&3&7&.&0&\color{Blue}{3}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0&0&.&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&\color{Blue}{1}&\phantom{.}&\color{Blue}{0}&\color{Blue}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&&1&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$27$$$'s are in $$$190$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$190-27 \cdot 7 = 190 - 189= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&3&7&.&0&3&\color{Purple}{7}&\phantom{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0&0&.&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&1&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&&\color{Purple}{1}&\color{Purple}{9}&\color{Purple}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$27$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-27 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&3&7&.&0&3&7&\color{OrangeRed}{0}&\phantom{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0&0&.&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&1&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&&1&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&\color{OrangeRed}{1}&\color{OrangeRed}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&0\\\hline\phantom{lll}&&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$27$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-27 \cdot 3 = 100 - 81= 19$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&3&7&.&0&3&7&0&\color{Chartreuse}{3}&\phantom{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0&0&.&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&1&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&&1&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&1&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&0\\\hline\phantom{lll}&&&&&&&\color{Chartreuse}{1}&\color{Chartreuse}{0}&\color{Chartreuse}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&8&1\\\hline\phantom{lll}&&&&&&&&1&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 10

How many $$$27$$$'s are in $$$190$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$190-27 \cdot 7 = 190 - 189= 1$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccccc}0&0&3&7&.&0&3&7&0&3&\color{Green}{7}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccc}1&0&0&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&1&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&&1&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&1&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&0\\\hline\phantom{lll}&&&&&&&1&0&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&8&1\\\hline\phantom{lll}&&&&&&&&\color{Green}{1}&\color{Green}{9}&\color{Green}{0}\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&&&&1\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1000}{27}=37. \overline{037}$$$

Answer: $$$\frac{1000}{27}=37.\overline{037}$$$


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