Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{600}{6}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\6&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}6&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

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

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$6-6 \cdot 1 = 6 - 6= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{DarkBlue}{1}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{DarkBlue}{6}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$6$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}1&\color{Chocolate}{0}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}6&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$6$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}1&0&\color{DarkMagenta}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}6&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkMagenta}{0}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$6$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}1&0&0&.&\color{Purple}{0}\end{array}&\\\color{Magenta}{6}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}6&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{0}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{600}{6}=100.0 \overline{}$$$

Answer: $$$\frac{600}{6}=100.0\overline{}$$$