Kesirden Ondalık Sayıya Dönüştürücü

Your input: convert $$$\frac{1200}{15}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\15&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$15$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-15 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{DarkBlue}{0}&\phantom{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{DarkBlue}{1}& 2 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$15$$$'s are in $$$12$$$?

The answer is $$$0$$$.

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

Now, $$$12-15 \cdot 0 = 12 - 0= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Purple}{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Purple}{1}&\color{Purple}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$15$$$'s are in $$$120$$$?

The answer is $$$8$$$.

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

Now, $$$120-15 \cdot 8 = 120 - 120= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Chartreuse}{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{2}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$15$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-15 \cdot 0 = 0 - 0= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&8&\color{OrangeRed}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&&\color{OrangeRed}{0}&\color{OrangeRed}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$15$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-15 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&8&0&.&\color{Green}{0}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&2&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Green}{0}&\phantom{.}&\color{Green}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1200}{15}=80.0 \overline{}$$$

Answer: $$$\frac{1200}{15}=80.0\overline{}$$$