Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{3600}{75}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\75&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}3&6&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$75$$$'s are in $$$3$$$?

The answer is $$$0$$$.

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

Now, $$$3-75 \cdot 0 = 3 - 0= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Red}{0}&\phantom{0}&\phantom{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{75}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Red}{3}& 6 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$75$$$'s are in $$$36$$$?

The answer is $$$0$$$.

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

Now, $$$36-75 \cdot 0 = 36 - 0= 36$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DarkCyan}{0}&\phantom{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{75}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&6& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{3}&\color{DarkCyan}{6}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$75$$$'s are in $$$360$$$?

The answer is $$$4$$$.

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

Now, $$$360-75 \cdot 4 = 360 - 300= 60$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{BlueViolet}{4}&\phantom{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{75}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&6&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{3}&\color{BlueViolet}{6}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&0&0&\phantom{.}\\\hline\phantom{lll}&6&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$75$$$'s are in $$$600$$$?

The answer is $$$8$$$.

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

Now, $$$600-75 \cdot 8 = 600 - 600= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&\color{Purple}{8}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{75}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&6&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&0&0&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{6}&\color{Purple}{0}&\color{Purple}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&6&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$75$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-75 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&8&.&\color{Peru}{0}\end{array}&\\\color{Magenta}{75}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&6&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}3&0&0&\phantom{.}\\\hline\phantom{lll}&6&0&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&6&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Peru}{0}&\phantom{.}&\color{Peru}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{3600}{75}=48.0 \overline{}$$$

Answer: $$$\frac{3600}{75}=48.0\overline{}$$$