Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{5200}{60}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\60&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}5&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$60$$$'s are in $$$5$$$?

The answer is $$$0$$$.

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

Now, $$$5-60 \cdot 0 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Red}{0}&\phantom{0}&\phantom{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Red}{5}& 2 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$60$$$'s are in $$$52$$$?

The answer is $$$0$$$.

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

Now, $$$52-60 \cdot 0 = 52 - 0= 52$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Chartreuse}{0}&\phantom{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&2& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{5}&\color{Chartreuse}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$60$$$'s are in $$$520$$$?

The answer is $$$8$$$.

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

Now, $$$520-60 \cdot 8 = 520 - 480= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{Violet}{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&2&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{5}&\color{Violet}{2}&\color{Violet}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&4&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$60$$$'s are in $$$400$$$?

The answer is $$$6$$$.

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

Now, $$$400-60 \cdot 6 = 400 - 360= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&\color{Peru}{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&2&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&\color{Peru}{4}&\color{Peru}{0}&\color{Peru}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&6&0&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$60$$$'s are in $$$400$$$?

The answer is $$$6$$$.

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

Now, $$$400-60 \cdot 6 = 400 - 360= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&6&.&\color{DarkMagenta}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&2&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&4&0&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&6&0&\phantom{.}\\\hline\phantom{lll}&&\color{DarkMagenta}{4}&\color{DarkMagenta}{0}&\phantom{.}&\color{DarkMagenta}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&6&\phantom{.}&0\\\hline\phantom{lll}&&&4&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$60$$$'s are in $$$400$$$?

The answer is $$$6$$$.

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

Now, $$$400-60 \cdot 6 = 400 - 360= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&6&.&6&\color{OrangeRed}{6}&\phantom{6}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&2&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&4&0&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&6&0&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&6&\phantom{.}&0\\\hline\phantom{lll}&&&\color{OrangeRed}{4}&\phantom{.}&\color{OrangeRed}{0}&\color{OrangeRed}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&6&0\\\hline\phantom{lll}&&&&&4&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$60$$$'s are in $$$400$$$?

The answer is $$$6$$$.

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

Now, $$$400-60 \cdot 6 = 400 - 360= 40$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&6&.&6&6&\color{DeepPink}{6}\end{array}&\\\color{Magenta}{60}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}5&2&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}4&8&0&\phantom{.}\\\hline\phantom{lll}&4&0&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&6&0&\phantom{.}\\\hline\phantom{lll}&&4&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&6&\phantom{.}&0\\\hline\phantom{lll}&&&4&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&6&0\\\hline\phantom{lll}&&&&&\color{DeepPink}{4}&\color{DeepPink}{0}&\color{DeepPink}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&6&0\\\hline\phantom{lll}&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{5200}{60}=86.6 \overline{6}$$$

Answer: $$$\frac{5200}{60}=86.6\overline{6}$$$