Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{4200}{54}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\54&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$54$$$'s are in $$$4$$$?

The answer is $$$0$$$.

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

Now, $$$4-54 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}\color{DarkMagenta}{0}&\phantom{0}&\phantom{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}\color{DarkMagenta}{4}& 2 \downarrow&0&0&.&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$54$$$'s are in $$$42$$$?

The answer is $$$0$$$.

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

Now, $$$42-54 \cdot 0 = 42 - 0= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&\color{OrangeRed}{0}&\phantom{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2& 0 \downarrow&0&.&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{4}&\color{OrangeRed}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&\color{DarkCyan}{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0& 0 \downarrow&.&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{4}&\color{DarkCyan}{2}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&\color{GoldenRod}{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.& 0 \downarrow&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&\color{GoldenRod}{4}&\color{GoldenRod}{2}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&4&2&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&7&.&\color{Violet}{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.&0& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{4}&\color{Violet}{2}&\phantom{.}&\color{Violet}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&7&\phantom{.}&8\\\hline\phantom{lll}&&&4&\phantom{.}&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&7&.&7&\color{Green}{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.&0&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&4&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&7&\phantom{.}&8\\\hline\phantom{lll}&&&\color{Green}{4}&\phantom{.}&\color{Green}{2}&\color{Green}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&7&8\\\hline\phantom{lll}&&&&&4&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&7&.&7&7&\color{Brown}{7}&\phantom{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.&0&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&4&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&7&\phantom{.}&8\\\hline\phantom{lll}&&&4&\phantom{.}&2&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&7&8\\\hline\phantom{lll}&&&&&\color{Brown}{4}&\color{Brown}{2}&\color{Brown}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&7&8\\\hline\phantom{lll}&&&&&&4&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&7&.&7&7&7&\color{Fuchsia}{7}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.&0&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&4&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&7&\phantom{.}&8\\\hline\phantom{lll}&&&4&\phantom{.}&2&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&7&8\\\hline\phantom{lll}&&&&&4&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&7&8\\\hline\phantom{lll}&&&&&&\color{Fuchsia}{4}&\color{Fuchsia}{2}&\color{Fuchsia}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&4&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&7&.&7&7&7&7&\color{Red}{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.&0&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&4&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&7&\phantom{.}&8\\\hline\phantom{lll}&&&4&\phantom{.}&2&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&7&8\\\hline\phantom{lll}&&&&&4&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&7&8\\\hline\phantom{lll}&&&&&&4&2&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&\color{Red}{4}&\color{Red}{2}&\color{Red}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&&4&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 10

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&7&.&7&7&7&7&7&\color{Peru}{7}&\phantom{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.&0&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&4&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&7&\phantom{.}&8\\\hline\phantom{lll}&&&4&\phantom{.}&2&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&7&8\\\hline\phantom{lll}&&&&&4&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&7&8\\\hline\phantom{lll}&&&&&&4&2&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&4&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&&\color{Peru}{4}&\color{Peru}{2}&\color{Peru}{0}\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&&&4&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 11

How many $$$54$$$'s are in $$$420$$$?

The answer is $$$7$$$.

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

Now, $$$420-54 \cdot 7 = 420 - 378= 42$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccccc}0&0&7&7&.&7&7&7&7&7&7&\color{Crimson}{7}\end{array}&\\\color{Magenta}{54}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccccc}4&2&0&0&.&0&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}3&7&8&\phantom{.}\\\hline\phantom{lll}&4&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&7&8&\phantom{.}\\\hline\phantom{lll}&&4&2&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&7&\phantom{.}&8\\\hline\phantom{lll}&&&4&\phantom{.}&2&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&7&8\\\hline\phantom{lll}&&&&&4&2&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&7&8\\\hline\phantom{lll}&&&&&&4&2&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&4&2&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&&4&2&0\\&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&&&\color{Crimson}{4}&\color{Crimson}{2}&\color{Crimson}{0}\\&&&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&&3&7&8\\\hline\phantom{lll}&&&&&&&&&&4&2\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: $$$\frac{4200}{54}=77.7 \overline{777}$$$

Answer: $$$\frac{4200}{54}=77.7\overline{777}$$$