Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{6700}{100}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{7}&\phantom{.}&\phantom{0}\end{array}&\\100&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}6&7&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$100$$$'s are in $$$6$$$?

The answer is $$$0$$$.

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

Now, $$$6-100 \cdot 0 = 6 - 0= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Purple}{0}&\phantom{0}&\phantom{6}&\phantom{7}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Purple}{6}& 7 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&7&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$100$$$'s are in $$$67$$$?

The answer is $$$0$$$.

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

Now, $$$67-100 \cdot 0 = 67 - 0= 67$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Chartreuse}{0}&\phantom{6}&\phantom{7}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&7& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{6}&\color{Chartreuse}{7}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}6&7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$100$$$'s are in $$$670$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$670-100 \cdot 6 = 670 - 600= 70$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Crimson}{6}&\phantom{7}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&7&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{6}&\color{Crimson}{7}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&0&0&\phantom{.}\\\hline\phantom{lll}&7&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$100$$$'s are in $$$700$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$700-100 \cdot 7 = 700 - 700= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{DarkCyan}{7}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&7&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}6&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&0&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkCyan}{7}&\color{DarkCyan}{0}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&7&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$100$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-100 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&7&.&\color{Blue}{0}\end{array}&\\\color{Magenta}{100}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&7&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}6&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&0&0&\phantom{.}\\\hline\phantom{lll}&7&0&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&7&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Blue}{0}&\phantom{.}&\color{Blue}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{6700}{100}=67.0$$$

Answer: $$$\frac{6700}{100}=67.0$$$