Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{600}{22}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{7}&\phantom{.}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\22&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}6&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$22$$$'s are in $$$6$$$?

The answer is $$$0$$$.

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

Now, $$$6-22 \cdot 0 = 6 - 0= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{Peru}{0}&\phantom{2}&\phantom{7}&\phantom{.}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{Peru}{6}& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$22$$$'s are in $$$60$$$?

The answer is $$$2$$$.

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

Now, $$$60-22 \cdot 2 = 60 - 44= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{BlueViolet}{2}&\phantom{7}&\phantom{.}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}6&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{6}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$22$$$'s are in $$$160$$$?

The answer is $$$7$$$.

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

Now, $$$160-22 \cdot 7 = 160 - 154= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&2&\color{SaddleBrown}{7}&\phantom{.}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}6&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{6}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$22$$$'s are in $$$60$$$?

The answer is $$$2$$$.

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

Now, $$$60-22 \cdot 2 = 60 - 44= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&2&7&.&\color{Green}{2}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}6&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&\color{Green}{6}&\phantom{.}&\color{Green}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&1&\phantom{.}&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$22$$$'s are in $$$160$$$?

The answer is $$$7$$$.

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

Now, $$$160-22 \cdot 7 = 160 - 154= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&2&7&.&2&\color{DarkBlue}{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}6&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&\color{DarkBlue}{1}&\phantom{.}&\color{DarkBlue}{6}&\color{DarkBlue}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&5&4\\\hline\phantom{lll}&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$22$$$'s are in $$$60$$$?

The answer is $$$2$$$.

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

Now, $$$60-22 \cdot 2 = 60 - 44= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&2&7&.&2&7&\color{DarkCyan}{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}6&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&1&\phantom{.}&6&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&5&4\\\hline\phantom{lll}&&&&&\color{DarkCyan}{6}&\color{DarkCyan}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$22$$$'s are in $$$160$$$?

The answer is $$$7$$$.

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

Now, $$$160-22 \cdot 7 = 160 - 154= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&2&7&.&2&7&2&\color{Crimson}{7}&\phantom{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}6&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&1&\phantom{.}&6&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&5&4\\\hline\phantom{lll}&&&&&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&\color{Crimson}{1}&\color{Crimson}{6}&\color{Crimson}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&5&4\\\hline\phantom{lll}&&&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$22$$$'s are in $$$60$$$?

The answer is $$$2$$$.

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

Now, $$$60-22 \cdot 2 = 60 - 44= 16$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&2&7&.&2&7&2&7&\color{DeepPink}{2}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}6&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}4&4&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&\phantom{.}&4\\\hline\phantom{lll}&&1&\phantom{.}&6&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&5&4\\\hline\phantom{lll}&&&&&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&5&4\\\hline\phantom{lll}&&&&&&&\color{DeepPink}{6}&\color{DeepPink}{0}\\&&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&4&4\\\hline\phantom{lll}&&&&&&&1&6\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{600}{22}=27.2 \overline{72}$$$

Answer: $$$\frac{600}{22}=27.2\overline{72}$$$