Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{16800}{200}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\200&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}1&6&8&0&0\end{array}}&\\&\begin{array}{lllll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$200$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Red}{0}&\phantom{0}&\phantom{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Red}{1}& 6 \downarrow&8&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$200$$$'s are in $$$16$$$?

The answer is $$$0$$$.

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

Now, $$$16-200 \cdot 0 = 16 - 0= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{Blue}{0}&\phantom{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6& 8 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{1}&\color{Blue}{6}&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&8&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$200$$$'s are in $$$168$$$?

The answer is $$$0$$$.

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

Now, $$$168-200 \cdot 0 = 168 - 0= 168$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{DeepPink}{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&8& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{1}&\color{DeepPink}{6}&\color{DeepPink}{8}&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&6&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$200$$$'s are in $$$1680$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$1680-200 \cdot 8 = 1680 - 1600= 80$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&\color{Crimson}{8}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&8&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&8&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{6}&\color{Crimson}{8}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&0&\phantom{.}\\\hline\phantom{lll}&&8&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$200$$$'s are in $$$800$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$800-200 \cdot 4 = 800 - 800= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&\color{Violet}{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&8&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&8&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&6&8&0&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&0&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{8}&\color{Violet}{0}&\color{Violet}{0}&\phantom{.}\\&-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&8&0&0&\phantom{.}\\\hline\phantom{lll}&&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$200$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&0&8&4&.&\color{DarkCyan}{0}\end{array}&\\\color{Magenta}{200}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&6&8&0&0&.&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&8&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}1&6&8&0&\phantom{.}\\-&\phantom{6}&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&6&0&0&\phantom{.}\\\hline\phantom{lll}&&8&0&0&\phantom{.}\\&-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&8&0&0&\phantom{.}\\\hline\phantom{lll}&&&&\color{DarkCyan}{0}&\phantom{.}&\color{DarkCyan}{0}\\&&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{16800}{200}=84.0$$$

Answer: $$$\frac{16800}{200}=84.0$$$