Bruch-zu-Dezimal-Rechner
Schritt für Schritt Brüche in Dezimalzahlen umwandeln
Der Rechner wandelt den gegebenen (echten oder unechten) Bruch oder die gemischte Zahl in eine Dezimalzahl um (eventuell mit Wiederholungen oder wiederkehrenden Zahlen), wobei die Schritte angezeigt werden.
Solution
Your input: convert 90090 into a decimal.
Write the problem in the special format:
−10.090−900
Step 1
How many 90's are in 9? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 9-0 \cdot 90 = 9 - 0= 9.
Bring down the next digit of the dividend.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Blue}{0}&\phantom{1}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Blue}{9}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}
Step 2
How many 90's are in 90? The answer is 1.
Write down the calculated result in the upper part of the table.
Now, 90-1 \cdot 90 = 90 - 90= 0.
Bring down the next digit of the dividend.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{GoldenRod}{1}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{9}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}
Step 3
How many 90's are in 0? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 0-0 \cdot 90 = 0 - 0= 0.
Bring down the next digit of the dividend.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&1&\color{DarkCyan}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&\phantom{.}\\\hline\phantom{lll}&\color{DarkCyan}{0}&\color{DarkCyan}{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 4
How many 90's are in 0? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 0-0 \cdot 90 = 0 - 0= 0.
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&1&0&.&\color{DarkBlue}{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}9&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&\color{DarkBlue}{0}&\phantom{.}&\color{DarkBlue}{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{900}{90}=10. \overline{0}
Answer: \frac{900}{90}=10.\overline{0}