Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{5400}{90}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\90&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}5&4&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$90$$$'s are in $$$5$$$?

The answer is $$$0$$$.

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

Now, $$$5-90 \cdot 0 = 5 - 0= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Green}{0}&\phantom{0}&\phantom{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Green}{5}& 4 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&4&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$90$$$'s are in $$$54$$$?

The answer is $$$0$$$.

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

Now, $$$54-90 \cdot 0 = 54 - 0= 54$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{SaddleBrown}{0}&\phantom{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&4& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{5}&\color{SaddleBrown}{4}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$90$$$'s are in $$$540$$$?

The answer is $$$6$$$.

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

Now, $$$540-90 \cdot 6 = 540 - 540= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Crimson}{6}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&4&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{5}&\color{Crimson}{4}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}5&4&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$90$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-90 \cdot 0 = 0 - 0= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{DarkBlue}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&4&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}5&4&0&\phantom{.}\\\hline\phantom{lll}&&\color{DarkBlue}{0}&\color{DarkBlue}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$90$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-90 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&0&.&\color{DeepPink}{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}5&4&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}5&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}5&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}5&4&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{DeepPink}{0}&\phantom{.}&\color{DeepPink}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{5400}{90}=60. \overline{0}$$$

Answer: $$$\frac{5400}{90}=60.\overline{0}$$$