Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{100}{15}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\15&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Crimson}{0}&\phantom{0}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Crimson}{1}& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$15$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-15 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{DarkBlue}{0}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$15$$$'s are in $$$100$$$?

The answer is $$$6$$$.

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

Now, $$$100-15 \cdot 6 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{SaddleBrown}{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{0}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$15$$$'s are in $$$100$$$?

The answer is $$$6$$$.

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

Now, $$$100-15 \cdot 6 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&.&\color{Chocolate}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&0&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{1}&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&\phantom{.}&9&0\\\hline\phantom{lll}&&1&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$15$$$'s are in $$$100$$$?

The answer is $$$6$$$.

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

Now, $$$100-15 \cdot 6 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&.&6&\color{Blue}{6}&\phantom{6}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&\phantom{.}&9&0\\\hline\phantom{lll}&&\color{Blue}{1}&\phantom{.}&\color{Blue}{0}&\color{Blue}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&9&\phantom{.}&0\\\hline\phantom{lll}&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$15$$$'s are in $$$100$$$?

The answer is $$$6$$$.

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

Now, $$$100-15 \cdot 6 = 100 - 90= 10$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&6&.&6&6&\color{DeepPink}{6}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}1&0&0&.&0&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&\phantom{.}&9&0\\\hline\phantom{lll}&&1&\phantom{.}&0&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&9&\phantom{.}&0\\\hline\phantom{lll}&&&&\color{DeepPink}{1}&\color{DeepPink}{0}&\color{DeepPink}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&9&0\\\hline\phantom{lll}&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{100}{15}=6.6 \overline{6}$$$

Answer: $$$\frac{100}{15}=6.6\overline{6}$$$