Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{1600}{22}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\22&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&6&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$22$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-22 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{Violet}{0}&\phantom{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{Violet}{1}& 6 \downarrow&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$22$$$'s are in $$$16$$$?

The answer is $$$0$$$.

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

Now, $$$16-22 \cdot 0 = 16 - 0= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{Purple}{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{6}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

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

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.

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

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.

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

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.

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

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.

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

Step 8

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

The answer is $$$2$$$.

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

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

Bring down the next digit of the dividend.

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

Step 9

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

The answer is $$$7$$$.

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

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

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

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1600}{22}=72.7 \overline{27}$$$

Answer: $$$\frac{1600}{22}=72.7\overline{27}$$$