Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{800}{11}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\11&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}8&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$11$$$'s are in $$$8$$$?

The answer is $$$0$$$.

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

Now, $$$8-11 \cdot 0 = 8 - 0= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{DarkBlue}{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{DarkBlue}{8}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$11$$$'s are in $$$80$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$80-11 \cdot 7 = 80 - 77= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Chocolate}{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}8&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{8}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$11$$$'s are in $$$30$$$?

The answer is $$$2$$$.

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

Now, $$$30-11 \cdot 2 = 30 - 22= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&7&\color{DarkMagenta}{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}8&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&7&\phantom{.}\\\hline\phantom{lll}&\color{DarkMagenta}{3}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&&8&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$11$$$'s are in $$$80$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$80-11 \cdot 7 = 80 - 77= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&7&2&.&\color{Purple}{7}&\phantom{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}8&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{8}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$11$$$'s are in $$$30$$$?

The answer is $$$2$$$.

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

Now, $$$30-11 \cdot 2 = 30 - 22= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&7&2&.&7&\color{BlueViolet}{2}&\phantom{7}&\phantom{2}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}8&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&&8&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&\phantom{.}&7\\\hline\phantom{lll}&&&&\color{BlueViolet}{3}&\color{BlueViolet}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&2\\\hline\phantom{lll}&&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$11$$$'s are in $$$80$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$80-11 \cdot 7 = 80 - 77= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&7&2&.&7&2&\color{Crimson}{7}&\phantom{2}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}8&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&&8&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&2\\\hline\phantom{lll}&&&&&\color{Crimson}{8}&\color{Crimson}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&7&7\\\hline\phantom{lll}&&&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$11$$$'s are in $$$30$$$?

The answer is $$$2$$$.

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

Now, $$$30-11 \cdot 2 = 30 - 22= 8$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&7&2&.&7&2&7&\color{DarkCyan}{2}\end{array}&\\\color{Magenta}{11}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}8&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&2&\phantom{.}\\\hline\phantom{lll}&&8&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&2\\\hline\phantom{lll}&&&&&8&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&7&7\\\hline\phantom{lll}&&&&&&\color{DarkCyan}{3}&\color{DarkCyan}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&2&2\\\hline\phantom{lll}&&&&&&&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{800}{11}=72. \overline{72}$$$

Answer: $$$\frac{800}{11}=72.\overline{72}$$$