Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{600}{9}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\9&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}6&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$9$$$'s are in $$$6$$$?

The answer is $$$0$$$.

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

Now, $$$6-9 \cdot 0 = 6 - 0= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Green}{0}&\phantom{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Green}{6}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$9$$$'s are in $$$60$$$?

The answer is $$$6$$$.

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

Now, $$$60-9 \cdot 6 = 60 - 54= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Chocolate}{6}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{6}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$9$$$'s are in $$$60$$$?

The answer is $$$6$$$.

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

Now, $$$60-9 \cdot 6 = 60 - 54= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&6&\color{GoldenRod}{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&\color{GoldenRod}{6}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$9$$$'s are in $$$60$$$?

The answer is $$$6$$$.

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

Now, $$$60-9 \cdot 6 = 60 - 54= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&6&6&.&\color{Purple}{6}&\phantom{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&4&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{6}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&\phantom{.}&4\\\hline\phantom{lll}&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$9$$$'s are in $$$60$$$?

The answer is $$$6$$$.

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

Now, $$$60-9 \cdot 6 = 60 - 54= 6$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&6&6&.&6&\color{DarkMagenta}{6}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}6&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}5&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&5&4&\phantom{.}\\\hline\phantom{lll}&&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&5&\phantom{.}&4\\\hline\phantom{lll}&&&&\color{DarkMagenta}{6}&\color{DarkMagenta}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&5&4\\\hline\phantom{lll}&&&&&6\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{600}{9}=66. \overline{6}$$$

Answer: $$$\frac{600}{9}=66.\overline{6}$$$