Υπολογιστής μετατροπής κλάσματος σε δεκαδικό

Your input: convert $$$\frac{1600}{21}$$$ into a decimal.

Write the problem in the special format:

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

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.

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

Step 2

How many $$$21$$$'s are in $$$16$$$?

The answer is $$$0$$$.

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

Now, $$$16-21 \cdot 0 = 16 - 0= 16$$$.

Bring down the next digit of the dividend.

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

Step 3

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.

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

Step 4

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.

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

Step 5

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.

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

Step 6

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}{ccccccccccccccccc}0&0&7&6&.&1&\color{DeepPink}{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0& 0 \downarrow&0&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&\color{DeepPink}{1}&\phantom{.}&\color{DeepPink}{9}&\color{DeepPink}{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{.}&8&9\\\hline\phantom{lll}&&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

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}{ccccccccccccccccc}0&0&7&6&.&1&9&\color{Peru}{0}&\phantom{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0& 0 \downarrow&0&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&8&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 8

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}{ccccccccccccccccc}0&0&7&6&.&1&9&0&\color{Chartreuse}{4}&\phantom{7}&\phantom{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0&0& 0 \downarrow&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&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{0}&\phantom{0}\\\phantom{lll}&&&&&&&0\\\hline\phantom{lll}&&&&&&\color{Chartreuse}{1}&\color{Chartreuse}{0}&\color{Chartreuse}{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}&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

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

Step 10

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}{ccccccccccccccccc}0&0&7&6&.&1&9&0&4&7&\color{Blue}{6}&\phantom{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0&0&0&0& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&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{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}&&&&&&&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{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&4&7\\\hline\phantom{lll}&&&&&&&&\color{Blue}{1}&\color{Blue}{3}&\color{Blue}{0}\\&&&&&&&-&\phantom{0}&\phantom{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 11

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}{ccccccccccccccccc}0&0&7&6&.&1&9&0&4&7&6&\color{Fuchsia}{1}&\phantom{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0&0&0&0&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&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{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}&&&&&&&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{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{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&\color{Fuchsia}{4}&\color{Fuchsia}{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 12

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}{ccccccccccccccccc}0&0&7&6&.&1&9&0&4&7&6&1&\color{DarkBlue}{9}&\phantom{0}&\phantom{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0&0&0&0&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&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{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}&&&&&&&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{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{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&4&0\\&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&2&1\\\hline\phantom{lll}&&&&&&&&&&\color{DarkBlue}{1}&\color{DarkBlue}{9}&\color{DarkBlue}{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 13

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}{ccccccccccccccccc}0&0&7&6&.&1&9&0&4&7&6&1&9&\color{Chocolate}{0}&\phantom{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0&0&0&0&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&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{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}&&&&&&&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{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{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&4&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{lll}&&&&&&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&&&&&&\color{Chocolate}{1}&\color{Chocolate}{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 14

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}{ccccccccccccccccc}0&0&7&6&.&1&9&0&4&7&6&1&9&0&\color{BlueViolet}{4}&\phantom{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0&0&0&0&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&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{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}&&&&&&&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{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{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&4&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{lll}&&&&&&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&&&&&&1&0\\&&&&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&&&&&0\\\hline\phantom{lll}&&&&&&&&&&&&\color{BlueViolet}{1}&\color{BlueViolet}{0}&\color{BlueViolet}{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 15

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}{ccccccccccccccccc}0&0&7&6&.&1&9&0&4&7&6&1&9&0&4&\color{Purple}{7}&\phantom{6}\end{array}&\\\color{Magenta}{21}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccccccccccccc}1&6&0&0&.&0&0&0&0&0&0&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllllllllllllll}-&\phantom{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{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{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{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{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{lll}1&4&7&\phantom{.}\\\hline\phantom{lll}&1&3&0&\phantom{.}\\-&\phantom{6}&\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&2&6&\phantom{.}\\\hline\phantom{lll}&&&4&\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{.}&1\\\hline\phantom{lll}&&&1&\phantom{.}&9&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{.}&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{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}&&&&&&&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{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{0}&\phantom{0}\\\phantom{lll}&&&&&&&&1&2&6\\\hline\phantom{lll}&&&&&&&&&&4&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{lll}&&&&&&&&&&1&8&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}&&&&&&&&&&&&&8&4\\\hline\phantom{lll}&&&&&&&&&&&&&\color{Purple}{1}&\color{Purple}{6}&\color{Purple}{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 16

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

The answer is $$$6$$$.

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

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

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

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1600}{21}=76. \overline{190476}$$$

Answer: $$$\frac{1600}{21}=76.\overline{190476}$$$