Calculatrice de fractions à décimales

Your input: convert $\frac{12300}{200}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{6}&\phantom{1}&\phantom{.}&\phantom{5}\end{array}&\\200&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&2&3&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $200$'s are in $1$? The answer is $0$.

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

Now, $1-0 \cdot 200 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{0}&\phantom{6}&\phantom{1}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Fuchsia}{1}& 2 \downarrow&3&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $200$'s are in $12$? The answer is $0$.

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

Now, $12-0 \cdot 200 = 12 - 0= 12$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Chocolate}{0}&\phantom{0}&\phantom{6}&\phantom{1}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2& 3 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{2}&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&3&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $200$'s are in $123$? The answer is $0$.

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

Now, $123-0 \cdot 200 = 123 - 0= 123$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Chartreuse}{0}&\phantom{6}&\phantom{1}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&3& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{2}&\color{Chartreuse}{3}&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $200$'s are in $1230$? The answer is $6$.

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

Now, $1230-6 \cdot 200 = 1230 - 1200= 30$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{DarkCyan}{6}&\phantom{1}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&3&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&3&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{1}&\color{DarkCyan}{2}&\color{DarkCyan}{3}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&3&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $200$'s are in $300$? The answer is $1$.

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

Now, $300-1 \cdot 200 = 300 - 200= 100$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&6&\color{Purple}{1}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&3&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&3&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&3&0&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{3}&\color{Purple}{0}&\color{Purple}{0}&\phantom{.}\\&-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&2&0&0&\phantom{.}\\\hline\phantom{lll}&&1&0&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $200$'s are in $1000$? The answer is $5$.

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

Now, $1000-5 \cdot 200 = 1000 - 1000= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&6&1&.&\color{Crimson}{5}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&2&3&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&3&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&2&3&0&\phantom{.}\\-&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&0&\phantom{.}\\\hline\phantom{lll}&&3&0&0&\phantom{.}\\&-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&2&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{Crimson}{1}&\color{Crimson}{0}&\color{Crimson}{0}&\phantom{.}&\color{Crimson}{0}\\&-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&1&0&0&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Since the remainder is $0$, then we are done.

Therefore, $\frac{12300}{200}=61.5$

Answer: $\frac{12300}{200}=61.5$