Calcolatrice da frazione a decimale

Your input: convert $$$\frac{100}{13}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{7}&\phantom{.}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}\end{array}&\\13&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$13$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-13 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

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

Step 2

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.

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

Step 3

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.

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

Step 4

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.

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

Step 5

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.

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

Step 6

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.

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

Step 7

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

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&0&7&.&6&9&2&3&\color{DeepPink}{0}&\phantom{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{lll}&&&&&&3&9\\\hline\phantom{lll}&&&&&&&\color{DeepPink}{1}&\color{DeepPink}{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 9

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&0&7&.&6&9&2&3&0&\color{Red}{7}&\phantom{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{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{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{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 10

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&0&7&.&6&9&2&3&0&7&\color{Chartreuse}{6}&\phantom{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{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{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{lll}&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&\color{Chartreuse}{9}&\color{Chartreuse}{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 11

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&0&7&.&6&9&2&3&0&7&6&\color{DarkMagenta}{9}&\phantom{2}&\phantom{3}&\phantom{0}&\phantom{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{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{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{lll}&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&9&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{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{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 12

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&0&7&.&6&9&2&3&0&7&6&9&\color{Brown}{2}&\phantom{3}&\phantom{0}&\phantom{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{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{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{lll}&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&9&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{lll}&&&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&&&\color{Brown}{3}&\color{Brown}{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 13

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&0&7&.&6&9&2&3&0&7&6&9&2&\color{Fuchsia}{3}&\phantom{0}&\phantom{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{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{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{lll}&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&9&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{lll}&&&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&&&3&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&2&6\\\hline\phantom{lll}&&&&&&&&&&&&\color{Fuchsia}{4}&\color{Fuchsia}{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 14

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&0&7&.&6&9&2&3&0&7&6&9&2&3&\color{GoldenRod}{0}&\phantom{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{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{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{lll}&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&9&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{lll}&&&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&&&3&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{lll}&&&&&&&&&&&&3&9\\\hline\phantom{lll}&&&&&&&&&&&&&\color{GoldenRod}{1}&\color{GoldenRod}{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 15

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

The answer is $$$7$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&7&.&6&9&2&3&0&7&6&9&2&3&0&\color{Purple}{7}\end{array}&\\\color{Magenta}{13}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&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}1&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}&0&\phantom{.}\\\hline\phantom{lll}1&0&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}&9&1&\phantom{.}\\\hline\phantom{lll}&&9&\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}&&7&\phantom{.}&8\\\hline\phantom{lll}&&1&\phantom{.}&2&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}&&1&\phantom{.}&1&7\\\hline\phantom{lll}&&&&&3&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&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{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{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{lll}&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&9&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{lll}&&&&&&&&&1&1&7\\\hline\phantom{lll}&&&&&&&&&&&3&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{lll}&&&&&&&&&&&&3&9\\\hline\phantom{lll}&&&&&&&&&&&&&1&0\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&0\\\hline\phantom{lll}&&&&&&&&&&&&&\color{Purple}{1}&\color{Purple}{0}&\color{Purple}{0}\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&9&1\\\hline\phantom{lll}&&&&&&&&&&&&&&&9\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: $$$\frac{100}{13}=7. \overline{692307}$$$

Answer: $$$\frac{100}{13}=7.\overline{692307}$$$