Calculatrice de fractions à décimales
Convertir des fractions en décimales étape par étape
La calculatrice convertit la fraction donnée (propre ou impropre) ou le nombre mixte en un nombre décimal (éventuellement, répétitif ou récurrent), avec les étapes indiquées.
Solution
Your input: convert 90090 into a decimal.
Write the problem in the special format:
\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\90&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}
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{SaddleBrown}{0}&\phantom{1}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{SaddleBrown}{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{Green}{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{Green}{9}&\color{Green}{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{Blue}{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{Blue}{0}&\color{Blue}{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{GoldenRod}{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{GoldenRod}{0}&\phantom{.}&\color{GoldenRod}{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}