Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{800}{30}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}8&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$30$$$'s are in $$$8$$$?

The answer is $$$0$$$.

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

Now, $$$8-30 \cdot 0 = 8 - 0= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{DarkBlue}{0}&\phantom{2}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{DarkBlue}{8}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$30$$$'s are in $$$80$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$80-30 \cdot 2 = 80 - 60= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Chocolate}{2}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{8}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}2&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$30$$$'s are in $$$200$$$?

The answer is $$$6$$$.

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

Now, $$$200-30 \cdot 6 = 200 - 180= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&2&\color{DarkMagenta}{6}&\phantom{.}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{2}&\color{DarkMagenta}{0}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$30$$$'s are in $$$200$$$?

The answer is $$$6$$$.

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

Now, $$$200-30 \cdot 6 = 200 - 180= 20$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&2&6&.&\color{Purple}{6}&\phantom{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}2&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{2}&\color{Purple}{0}&\phantom{.}&\color{Purple}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&0\\\hline\phantom{lll}&&2&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$30$$$'s are in $$$200$$$?

The answer is $$$6$$$.

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

Now, $$$200-30 \cdot 6 = 200 - 180= 20$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&2&6&.&6&\color{BlueViolet}{6}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}2&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}1&8&0&\phantom{.}\\\hline\phantom{lll}&2&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&0\\\hline\phantom{lll}&&\color{BlueViolet}{2}&\phantom{.}&\color{BlueViolet}{0}&\color{BlueViolet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{800}{30}=26. \overline{6}$$$

Answer: $$$\frac{800}{30}=26.\overline{6}$$$