Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{900}{40}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\40&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$40$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-40 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Purple}{0}&\phantom{2}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Purple}{9}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$40$$$'s are in $$$90$$$?

The answer is $$$2$$$.

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

Now, $$$90-40 \cdot 2 = 90 - 80= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{Brown}{2}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{9}&\color{Brown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$40$$$'s are in $$$100$$$?

The answer is $$$2$$$.

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

Now, $$$100-40 \cdot 2 = 100 - 80= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&2&\color{DeepPink}{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{1}&\color{DeepPink}{0}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&8&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$40$$$'s are in $$$200$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$200-40 \cdot 5 = 200 - 200= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&2&2&.&\color{BlueViolet}{5}\end{array}&\\\color{Magenta}{40}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&8&0&\phantom{.}\\\hline\phantom{lll}&\color{BlueViolet}{2}&\color{BlueViolet}{0}&\phantom{.}&\color{BlueViolet}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&2&0&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{900}{40}=22.5$$$

Answer: $$$\frac{900}{40}=22.5$$$