Murtoluvusta desimaaliluvuksi -laskin

Your input: convert $$$\frac{700}{12}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{5}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\12&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}7&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$12$$$'s are in $$$7$$$?

The answer is $$$0$$$.

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

Now, $$$7-12 \cdot 0 = 7 - 0= 7$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{DarkBlue}{0}&\phantom{5}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{DarkBlue}{7}& 0 \downarrow&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$12$$$'s are in $$$70$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$70-12 \cdot 5 = 70 - 60= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Chocolate}{5}&\phantom{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}7&0& 0 \downarrow&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{7}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$12$$$'s are in $$$100$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$100-12 \cdot 8 = 100 - 96= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&5&\color{DarkMagenta}{8}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}7&0&0&.& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{1}&\color{DarkMagenta}{0}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&5&8&.&\color{Purple}{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}7&0&0&.&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{4}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&5&8&.&3&\color{BlueViolet}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}7&0&0&.&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&\color{BlueViolet}{4}&\color{BlueViolet}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&6\\\hline\phantom{lll}&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&5&8&.&3&3&\color{Crimson}{3}&\phantom{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}7&0&0&.&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&6\\\hline\phantom{lll}&&&&&\color{Crimson}{4}&\color{Crimson}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&6\\\hline\phantom{lll}&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$12$$$'s are in $$$40$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$40-12 \cdot 3 = 40 - 36= 4$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&5&8&.&3&3&3&\color{DarkCyan}{3}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}7&0&0&.&0&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}6&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&9&6&\phantom{.}\\\hline\phantom{lll}&&4&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&6\\\hline\phantom{lll}&&&&&4&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&6\\\hline\phantom{lll}&&&&&&\color{DarkCyan}{4}&\color{DarkCyan}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&3&6\\\hline\phantom{lll}&&&&&&&4\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{700}{12}=58.33 \overline{3}$$$

Answer: $$$\frac{700}{12}=58.33\overline{3}$$$