Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{900}{13}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{6}&\phantom{9}&\phantom{.}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\13&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$13$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-13 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}\color{SaddleBrown}{0}&\phantom{6}&\phantom{9}&\phantom{.}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}\color{SaddleBrown}{9}& 0 \downarrow&0&.&0&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$13$$$'s are in $$$90$$$?

The answer is $$$6$$$.

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

Now, $$$90-13 \cdot 6 = 90 - 78= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&\color{BlueViolet}{6}&\phantom{9}&\phantom{.}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0& 0 \downarrow&.&0&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{9}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$13$$$'s are in $$$120$$$?

The answer is $$$9$$$.

Write down $$$9$$$ in the upper part of the table.

Now, $$$120-13 \cdot 9 = 120 - 117= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&\color{Fuchsia}{9}&\phantom{.}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.& 0 \downarrow&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}\color{Fuchsia}{1}&\color{Fuchsia}{2}&\color{Fuchsia}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$13$$$'s are in $$$30$$$?

The answer is $$$2$$$.

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

Now, $$$30-13 \cdot 2 = 30 - 26= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&\color{Blue}{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0& 0 \downarrow&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&\color{Blue}{3}&\phantom{.}&\color{Blue}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$13$$$'s are in $$$40$$$?

The answer is $$$3$$$.

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

Now, $$$40-13 \cdot 3 = 40 - 39= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&\color{Violet}{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0& 0 \downarrow&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&\color{Violet}{4}&\color{Violet}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$13$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-13 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&\color{Peru}{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0& 0 \downarrow&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&\color{Peru}{1}&\color{Peru}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$13$$$'s are in $$$100$$$?

The answer is $$$7$$$.

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

Now, $$$100-13 \cdot 7 = 100 - 91= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&\color{Brown}{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0& 0 \downarrow&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&\color{Brown}{1}&\color{Brown}{0}&\color{Brown}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$13$$$'s are in $$$90$$$?

The answer is $$$6$$$.

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

Now, $$$90-13 \cdot 6 = 90 - 78= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&\color{OrangeRed}{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0& 0 \downarrow&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&\color{OrangeRed}{9}&\color{OrangeRed}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&1&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$13$$$'s are in $$$120$$$?

The answer is $$$9$$$.

Write down $$$9$$$ in the upper part of the table.

Now, $$$120-13 \cdot 9 = 120 - 117= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&6&\color{Chocolate}{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0&0& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&\color{Chocolate}{1}&\color{Chocolate}{2}&\color{Chocolate}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 10

How many $$$13$$$'s are in $$$30$$$?

The answer is $$$2$$$.

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

Now, $$$30-13 \cdot 2 = 30 - 26= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&6&9&\color{Crimson}{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0&0&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&1&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&\color{Crimson}{3}&\color{Crimson}{0}\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&2&6\\\hline\phantom{lll}&&&&&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 11

How many $$$13$$$'s are in $$$40$$$?

The answer is $$$3$$$.

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

Now, $$$40-13 \cdot 3 = 40 - 39= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&6&9&2&\color{DeepPink}{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0&0&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&1&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&2&6\\\hline\phantom{lll}&&&&&&&&&&\color{DeepPink}{4}&\color{DeepPink}{0}\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&3&9\\\hline\phantom{lll}&&&&&&&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 12

How many $$$13$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-13 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&6&9&2&3&\color{Purple}{0}&\phantom{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0&0&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&1&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&2&6\\\hline\phantom{lll}&&&&&&&&&&4&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&3&9\\\hline\phantom{lll}&&&&&&&&&&&\color{Purple}{1}&\color{Purple}{0}\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&0\\\hline\phantom{lll}&&&&&&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 13

How many $$$13$$$'s are in $$$100$$$?

The answer is $$$7$$$.

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

Now, $$$100-13 \cdot 7 = 100 - 91= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&6&9&2&3&0&\color{Red}{7}&\phantom{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0&0&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&1&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&2&6\\\hline\phantom{lll}&&&&&&&&&&4&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&3&9\\\hline\phantom{lll}&&&&&&&&&&&1&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&0\\\hline\phantom{lll}&&&&&&&&&&&\color{Red}{1}&\color{Red}{0}&\color{Red}{0}\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 14

How many $$$13$$$'s are in $$$90$$$?

The answer is $$$6$$$.

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

Now, $$$90-13 \cdot 6 = 90 - 78= 12$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&6&9&2&3&0&7&\color{DarkCyan}{6}&\phantom{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0&0&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&1&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&2&6\\\hline\phantom{lll}&&&&&&&&&&4&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&3&9\\\hline\phantom{lll}&&&&&&&&&&&1&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&0\\\hline\phantom{lll}&&&&&&&&&&&1&0&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&&&&&\color{DarkCyan}{9}&\color{DarkCyan}{0}\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&&&&&&&1&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 15

How many $$$13$$$'s are in $$$120$$$?

The answer is $$$9$$$.

Write down $$$9$$$ in the upper part of the table.

Now, $$$120-13 \cdot 9 = 120 - 117= 3$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&6&9&.&2&3&0&7&6&9&2&3&0&7&6&\color{DarkMagenta}{9}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}9&0&0&.&0&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}7&8&\phantom{.}\\\hline\phantom{lll}1&2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&1&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&6\\\hline\phantom{lll}&&&&4&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&3&9\\\hline\phantom{lll}&&&&&1&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&0\\\hline\phantom{lll}&&&&&1&0&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&1&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&2&6\\\hline\phantom{lll}&&&&&&&&&&4&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&3&9\\\hline\phantom{lll}&&&&&&&&&&&1&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&0\\\hline\phantom{lll}&&&&&&&&&&&1&0&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&&&&&9&0\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&7&8\\\hline\phantom{lll}&&&&&&&&&&&&&\color{DarkMagenta}{1}&\color{DarkMagenta}{2}&\color{DarkMagenta}{0}\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&&&&&&&3\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: $$$\frac{900}{13}=69. \overline{230769}$$$

Answer: $$$\frac{900}{13}=69.\overline{230769}$$$