Bruch-zu-Dezimal-Rechner

Your input: convert $\frac{900}{22}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{4}&\phantom{0}&\phantom{.}&\phantom{9}&\phantom{0}&\phantom{9}&\phantom{0}&\phantom{9}\end{array}&\\22&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $22$'s are in $9$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $9-0 \cdot 22 = 9 - 0= 9$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}\color{DarkCyan}{0}&\phantom{4}&\phantom{0}&\phantom{.}&\phantom{9}&\phantom{0}&\phantom{9}&\phantom{0}&\phantom{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}\color{DarkCyan}{9}& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $22$'s are in $90$? The answer is $4$.

Write down the calculated result in the upper part of the table.

Now, $90-4 \cdot 22 = 90 - 88= 2$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&\color{Brown}{4}&\phantom{0}&\phantom{.}&\phantom{9}&\phantom{0}&\phantom{9}&\phantom{0}&\phantom{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}9&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{9}&\color{Brown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $22$'s are in $20$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $20-0 \cdot 22 = 20 - 0= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&4&\color{Fuchsia}{0}&\phantom{.}&\phantom{9}&\phantom{0}&\phantom{9}&\phantom{0}&\phantom{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}9&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&\color{Fuchsia}{2}&\color{Fuchsia}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $22$'s are in $200$? The answer is $9$.

Write down the calculated result in the upper part of the table.

Now, $200-9 \cdot 22 = 200 - 198= 2$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&4&0&.&\color{DeepPink}{9}&\phantom{0}&\phantom{9}&\phantom{0}&\phantom{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}9&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&\color{DeepPink}{2}&\color{DeepPink}{0}&\phantom{.}&\color{DeepPink}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&9&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $22$'s are in $20$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $20-0 \cdot 22 = 20 - 0= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&4&0&.&9&\color{Chocolate}{0}&\phantom{9}&\phantom{0}&\phantom{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}9&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&9&\phantom{.}&8\\\hline\phantom{lll}&&&&\color{Chocolate}{2}&\color{Chocolate}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&2&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $22$'s are in $200$? The answer is $9$.

Write down the calculated result in the upper part of the table.

Now, $200-9 \cdot 22 = 200 - 198= 2$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&4&0&.&9&0&\color{Blue}{9}&\phantom{0}&\phantom{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}9&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&9&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&\color{Blue}{2}&\color{Blue}{0}&\color{Blue}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&9&8\\\hline\phantom{lll}&&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 7

How many $22$'s are in $20$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $20-0 \cdot 22 = 20 - 0= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&4&0&.&9&0&9&\color{Green}{0}&\phantom{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}9&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&9&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&2&0&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&9&8\\\hline\phantom{lll}&&&&&&\color{Green}{2}&\color{Green}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&0\\\hline\phantom{lll}&&&&&&2&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 8

How many $22$'s are in $200$? The answer is $9$.

Write down the calculated result in the upper part of the table.

Now, $200-9 \cdot 22 = 200 - 198= 2$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccccc}0&4&0&.&9&0&9&0&\color{Violet}{9}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccc}9&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&8&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&9&\phantom{.}&8\\\hline\phantom{lll}&&&&2&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&2&0&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&1&9&8\\\hline\phantom{lll}&&&&&&2&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&0\\\hline\phantom{lll}&&&&&&\color{Violet}{2}&\color{Violet}{0}&\color{Violet}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&9&8\\\hline\phantom{lll}&&&&&&&&2\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{900}{22}=40.9 \overline{09}$

Answer: $\frac{900}{22}=40.9\overline{09}$