Υπολογιστής μετατροπής κλάσματος σε δεκαδικό
Μετατρέψτε κλάσματα σε δεκαδικούς αριθμούς βήμα προς βήμα
Η αριθμομηχανή θα μετατρέψει το δοθέν κλάσμα (γνήσιο ή καταχρηστικό) ή μεικτό αριθμό σε δεκαδικό αριθμό (ενδεχομένως περιοδικό), με εμφάνιση των βημάτων.
Solution
Your input: convert $$$\frac{800}{9}$$$ into a decimal.
Write the problem in the special format:
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{8}&\phantom{8}&\phantom{.}&\phantom{8}&\phantom{8}\end{array}&\\9&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}8&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 1
How many $$$9$$$'s are in $$$8$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$8-9 \cdot 0 = 8 - 0= 8$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Chartreuse}{0}&\phantom{8}&\phantom{8}&\phantom{.}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Chartreuse}{8}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 2
How many $$$9$$$'s are in $$$80$$$?
The answer is $$$8$$$.
Write down $$$8$$$ in the upper part of the table.
Now, $$$80-9 \cdot 8 = 80 - 72= 8$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Green}{8}&\phantom{8}&\phantom{.}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Green}{8}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}7&2&\phantom{.}\\\hline\phantom{lll}&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 3
How many $$$9$$$'s are in $$$80$$$?
The answer is $$$8$$$.
Write down $$$8$$$ in the upper part of the table.
Now, $$$80-9 \cdot 8 = 80 - 72= 8$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&8&\color{Purple}{8}&\phantom{.}&\phantom{8}&\phantom{8}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}7&2&\phantom{.}\\\hline\phantom{lll}&\color{Purple}{8}&\color{Purple}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&&8&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 4
How many $$$9$$$'s are in $$$80$$$?
The answer is $$$8$$$.
Write down $$$8$$$ in the upper part of the table.
Now, $$$80-9 \cdot 8 = 80 - 72= 8$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&8&8&.&\color{Violet}{8}&\phantom{8}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}7&2&\phantom{.}\\\hline\phantom{lll}&8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{8}&\phantom{.}&\color{Violet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 5
How many $$$9$$$'s are in $$$80$$$?
The answer is $$$8$$$.
Write down $$$8$$$ in the upper part of the table.
Now, $$$80-9 \cdot 8 = 80 - 72= 8$$$.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&8&8&.&8&\color{Brown}{8}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}8&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}7&2&\phantom{.}\\\hline\phantom{lll}&8&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&7&2&\phantom{.}\\\hline\phantom{lll}&&8&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&7&\phantom{.}&2\\\hline\phantom{lll}&&&&\color{Brown}{8}&\color{Brown}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&7&2\\\hline\phantom{lll}&&&&&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$
As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{800}{9}=88. \overline{8}$$$
Answer: $$$\frac{800}{9}=88.\overline{8}$$$