Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{700}{27}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{5}&\phantom{.}&\phantom{9}&\phantom{2}&\phantom{5}&\phantom{9}&\phantom{2}&\phantom{5}\end{array}&\\27&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}7&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$27$$$'s are in $$$7$$$?

The answer is $$$0$$$.

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

Now, $$$7-27 \cdot 0 = 7 - 0= 7$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{Blue}{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{9}&\phantom{2}&\phantom{5}&\phantom{9}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{Blue}{7}& 0 \downarrow&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$27$$$'s are in $$$70$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$70-27 \cdot 2 = 70 - 54= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{Green}{2}&\phantom{5}&\phantom{.}&\phantom{9}&\phantom{2}&\phantom{5}&\phantom{9}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0& 0 \downarrow&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{7}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$27$$$'s are in $$$160$$$?

The answer is $$$5$$$.

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

Now, $$$160-27 \cdot 5 = 160 - 135= 25$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&2&\color{Purple}{5}&\phantom{.}&\phantom{9}&\phantom{2}&\phantom{5}&\phantom{9}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0&0&.& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{6}&\color{Purple}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&5&\phantom{.}\\\hline\phantom{lll}&2&5&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$27$$$'s are in $$$250$$$?

The answer is $$$9$$$.

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

Now, $$$250-27 \cdot 9 = 250 - 243= 7$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&2&5&.&\color{Brown}{9}&\phantom{2}&\phantom{5}&\phantom{9}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0&0&.&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&5&\phantom{.}\\\hline\phantom{lll}&\color{Brown}{2}&\color{Brown}{5}&\phantom{.}&\color{Brown}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&4&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$27$$$'s are in $$$70$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$70-27 \cdot 2 = 70 - 54= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&2&5&.&9&\color{DarkMagenta}{2}&\phantom{5}&\phantom{9}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0&0&.&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&5&\phantom{.}\\\hline\phantom{lll}&2&5&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&4&\phantom{.}&3\\\hline\phantom{lll}&&&&\color{DarkMagenta}{7}&\color{DarkMagenta}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&4\\\hline\phantom{lll}&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$27$$$'s are in $$$160$$$?

The answer is $$$5$$$.

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

Now, $$$160-27 \cdot 5 = 160 - 135= 25$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&2&5&.&9&2&\color{Chocolate}{5}&\phantom{9}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0&0&.&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&5&\phantom{.}\\\hline\phantom{lll}&2&5&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&4&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&4\\\hline\phantom{lll}&&&&\color{Chocolate}{1}&\color{Chocolate}{6}&\color{Chocolate}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&3&5\\\hline\phantom{lll}&&&&&2&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$27$$$'s are in $$$250$$$?

The answer is $$$9$$$.

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

Now, $$$250-27 \cdot 9 = 250 - 243= 7$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&2&5&.&9&2&5&\color{Violet}{9}&\phantom{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0&0&.&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&5&\phantom{.}\\\hline\phantom{lll}&2&5&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&4&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&4\\\hline\phantom{lll}&&&&1&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&3&5\\\hline\phantom{lll}&&&&&\color{Violet}{2}&\color{Violet}{5}&\color{Violet}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&4&3\\\hline\phantom{lll}&&&&&&&7&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$27$$$'s are in $$$70$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$70-27 \cdot 2 = 70 - 54= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&2&5&.&9&2&5&9&\color{Red}{2}&\phantom{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0&0&.&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&5&\phantom{.}\\\hline\phantom{lll}&2&5&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&4&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&4\\\hline\phantom{lll}&&&&1&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&3&5\\\hline\phantom{lll}&&&&&2&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&4&3\\\hline\phantom{lll}&&&&&&&\color{Red}{7}&\color{Red}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&5&4\\\hline\phantom{lll}&&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$27$$$'s are in $$$160$$$?

The answer is $$$5$$$.

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

Now, $$$160-27 \cdot 5 = 160 - 135= 25$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&2&5&.&9&2&5&9&2&\color{GoldenRod}{5}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}7&0&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&3&5&\phantom{.}\\\hline\phantom{lll}&2&5&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&4&\phantom{.}&3\\\hline\phantom{lll}&&&&7&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&4\\\hline\phantom{lll}&&&&1&6&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&3&5\\\hline\phantom{lll}&&&&&2&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&4&3\\\hline\phantom{lll}&&&&&&&7&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&5&4\\\hline\phantom{lll}&&&&&&&\color{GoldenRod}{1}&\color{GoldenRod}{6}&\color{GoldenRod}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&3&5\\\hline\phantom{lll}&&&&&&&&2&5\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{700}{27}=25. \overline{925}$$$

Answer: $$$\frac{700}{27}=25.\overline{925}$$$