Calculatrice de fractions à décimales

Your input: convert $\frac{1100}{44}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\44&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&1&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $44$'s are in $1$? The answer is $0$.

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

Now, $1-0 \cdot 44 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{BlueViolet}{0}&\phantom{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{44}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{BlueViolet}{1}& 1 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $44$'s are in $11$? The answer is $0$.

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

Now, $11-0 \cdot 44 = 11 - 0= 11$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DarkCyan}{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{44}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&1& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{1}&\color{DarkCyan}{1}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $44$'s are in $110$? The answer is $2$.

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

Now, $110-2 \cdot 44 = 110 - 88= 22$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Purple}{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{44}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&1&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{1}&\color{Purple}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&8&8&\phantom{.}\\\hline\phantom{lll}&2&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $44$'s are in $220$? The answer is $5$.

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

Now, $220-5 \cdot 44 = 220 - 220= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&\color{SaddleBrown}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{44}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&1&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&8&8&\phantom{.}\\\hline\phantom{lll}&\color{SaddleBrown}{2}&\color{SaddleBrown}{2}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&2&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $44$'s are in $0$? The answer is $0$.

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

Now, $0-0 \cdot 44 = 0 - 0= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&2&5&.&\color{Blue}{0}\end{array}&\\\color{Magenta}{44}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&1&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&8&8&\phantom{.}\\\hline\phantom{lll}&2&2&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&2&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Blue}{0}&\phantom{.}&\color{Blue}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{1100}{44}=25.0 \overline{}$

Answer: $\frac{1100}{44}=25.0\overline{}$