Calculadora de fracción a decimal

Your input: convert $$$\frac{100}{21}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{4}&\phantom{.}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\21&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$21$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-21 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}\color{GoldenRod}{0}&\phantom{0}&\phantom{4}&\phantom{.}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}\color{GoldenRod}{1}& 0 \downarrow&0&.&0&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$21$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-21 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&\color{Chocolate}{0}&\phantom{4}&\phantom{.}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&0& 0 \downarrow&.&0&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$21$$$'s are in $$$100$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$100-21 \cdot 4 = 100 - 84= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&\color{DarkMagenta}{4}&\phantom{.}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&0&0&.& 0 \downarrow&0&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{1}&\color{DarkMagenta}{0}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$21$$$'s are in $$$160$$$?

The answer is $$$7$$$.

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

Now, $$$160-21 \cdot 7 = 160 - 147= 13$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&\color{Brown}{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&0&0&.&0& 0 \downarrow&0&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&4&\phantom{.}\\\hline\phantom{lll}&\color{Brown}{1}&\color{Brown}{6}&\phantom{.}&\color{Brown}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$21$$$'s are in $$$130$$$?

The answer is $$$6$$$.

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

Now, $$$130-21 \cdot 6 = 130 - 126= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&\color{Green}{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&0&0&.&0&0& 0 \downarrow&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&\color{Green}{1}&\phantom{.}&\color{Green}{3}&\color{Green}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&2&6\\\hline\phantom{lll}&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$21$$$'s are in $$$40$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$40-21 \cdot 1 = 40 - 21= 19$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&\color{Blue}{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccccccc}1&0&0&.&0&0&0& 0 \downarrow&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&\phantom{.}&2&6\\\hline\phantom{lll}&&&&&\color{Blue}{4}&\color{Blue}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$21$$$'s are in $$$190$$$?

The answer is $$$9$$$.

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

Now, $$$190-21 \cdot 9 = 190 - 189= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&\color{Violet}{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&\color{Violet}{1}&\color{Violet}{9}&\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{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$21$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-21 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&\color{DarkCyan}{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&9\\\hline\phantom{lll}&&&&&&&\color{DarkCyan}{1}&\color{DarkCyan}{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 $$$21$$$'s are in $$$100$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$100-21 \cdot 4 = 100 - 84= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&0&\color{SaddleBrown}{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&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{SaddleBrown}{1}&\color{SaddleBrown}{0}&\color{SaddleBrown}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 10

How many $$$21$$$'s are in $$$160$$$?

The answer is $$$7$$$.

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

Now, $$$160-21 \cdot 7 = 160 - 147= 13$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&0&4&\color{Purple}{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&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}&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&\color{Purple}{1}&\color{Purple}{6}&\color{Purple}{0}\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&4&7\\\hline\phantom{lll}&&&&&&&&&1&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 11

How many $$$21$$$'s are in $$$130$$$?

The answer is $$$6$$$.

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

Now, $$$130-21 \cdot 6 = 130 - 126= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&0&4&7&\color{BlueViolet}{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&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}&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&1&6&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&4&7\\\hline\phantom{lll}&&&&&&&&&\color{BlueViolet}{1}&\color{BlueViolet}{3}&\color{BlueViolet}{0}\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&&4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 12

How many $$$21$$$'s are in $$$40$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$40-21 \cdot 1 = 40 - 21= 19$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&0&4&7&6&\color{Crimson}{1}&\phantom{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&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}&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&1&6&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&4&7\\\hline\phantom{lll}&&&&&&&&&1&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&&\color{Crimson}{4}&\color{Crimson}{0}\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&2&1\\\hline\phantom{lll}&&&&&&&&&&&1&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 13

How many $$$21$$$'s are in $$$190$$$?

The answer is $$$9$$$.

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

Now, $$$190-21 \cdot 9 = 190 - 189= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&0&4&7&6&1&\color{Red}{9}&\phantom{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&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}&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&1&6&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&4&7\\\hline\phantom{lll}&&&&&&&&&1&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&&4&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&2&1\\\hline\phantom{lll}&&&&&&&&&&&\color{Red}{1}&\color{Red}{9}&\color{Red}{0}\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&&&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 14

How many $$$21$$$'s are in $$$10$$$?

The answer is $$$0$$$.

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

Now, $$$10-21 \cdot 0 = 10 - 0= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&0&4&7&6&1&9&\color{DeepPink}{0}&\phantom{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&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}&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&1&6&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&4&7\\\hline\phantom{lll}&&&&&&&&&1&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&&4&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&2&1\\\hline\phantom{lll}&&&&&&&&&&&1&9&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&&&&&&&\color{DeepPink}{1}&\color{DeepPink}{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 $$$21$$$'s are in $$$100$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$100-21 \cdot 4 = 100 - 84= 16$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccccccc}0&0&4&.&7&6&1&9&0&4&7&6&1&9&0&\color{OrangeRed}{4}\end{array}&\\\color{Magenta}{21}&\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}&8&4&\phantom{.}\\\hline\phantom{lll}&1&6&\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{0}\\\phantom{lll}&1&4&\phantom{.}&7\\\hline\phantom{lll}&&1&\phantom{.}&3&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{.}&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{0}\\\phantom{lll}&&&&&2&1\\\hline\phantom{lll}&&&&&1&9&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&8&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}&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&1&6&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&4&7\\\hline\phantom{lll}&&&&&&&&&1&3&0\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&&4&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&2&1\\\hline\phantom{lll}&&&&&&&&&&&1&9&0\\&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&&&&&&&1&0\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&0\\\hline\phantom{lll}&&&&&&&&&&&&&\color{OrangeRed}{1}&\color{OrangeRed}{0}&\color{OrangeRed}{0}\\&&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&&&&&&&1&6\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: $$$\frac{100}{21}=4. \overline{761904}$$$

Answer: $$$\frac{100}{21}=4.\overline{761904}$$$