Bruch-zu-Dezimalzahl-Rechner

Your input: convert $$$\frac{7200}{90}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\90&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}7&2&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$90$$$'s are in $$$7$$$?

The answer is $$$0$$$.

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

Now, $$$7-90 \cdot 0 = 7 - 0= 7$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{SaddleBrown}{0}&\phantom{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{SaddleBrown}{7}& 2 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&2&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$90$$$'s are in $$$72$$$?

The answer is $$$0$$$.

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

Now, $$$72-90 \cdot 0 = 72 - 0= 72$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Blue}{0}&\phantom{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}7&2& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{7}&\color{Blue}{2}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}7&2&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$90$$$'s are in $$$720$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$720-90 \cdot 8 = 720 - 720= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{OrangeRed}{8}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}7&2&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{7}&\color{OrangeRed}{2}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}7&2&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&8&\color{Chocolate}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}7&2&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}7&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}7&2&0&\phantom{.}\\\hline\phantom{lll}&&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

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

The answer is $$$0$$$.

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&8&0&.&\color{Red}{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}7&2&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&2&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}7&2&0&\phantom{.}\\-&\phantom{2}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}7&2&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Red}{0}&\phantom{.}&\color{Red}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{7200}{90}=80. \overline{0}$$$

Answer: $$$\frac{7200}{90}=80.\overline{0}$$$