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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 $$$\frac{300}{9}$$$ into a decimal.
Write the problem in the special format:
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\9&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}3&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 1
How many $$$9$$$'s are in $$$3$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$3-9 \cdot 0 = 3 - 0= 3$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Peru}{0}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Peru}{3}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 2
How many $$$9$$$'s are in $$$30$$$?
The answer is $$$3$$$.
Write down $$$3$$$ in the upper part of the table.
Now, $$$30-9 \cdot 3 = 30 - 27= 3$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{BlueViolet}{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{BlueViolet}{3}&\color{BlueViolet}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 3
How many $$$9$$$'s are in $$$30$$$?
The answer is $$$3$$$.
Write down $$$3$$$ in the upper part of the table.
Now, $$$30-9 \cdot 3 = 30 - 27= 3$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&3&\color{SaddleBrown}{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}&\color{SaddleBrown}{3}&\color{SaddleBrown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 4
How many $$$9$$$'s are in $$$30$$$?
The answer is $$$3$$$.
Write down $$$3$$$ in the upper part of the table.
Now, $$$30-9 \cdot 3 = 30 - 27= 3$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&3&3&.&\color{Green}{3}&\phantom{3}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&\phantom{.}\\\hline\phantom{lll}&&\color{Green}{3}&\phantom{.}&\color{Green}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&7\\\hline\phantom{lll}&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 5
How many $$$9$$$'s are in $$$30$$$?
The answer is $$$3$$$.
Write down $$$3$$$ in the upper part of the table.
Now, $$$30-9 \cdot 3 = 30 - 27= 3$$$.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&3&3&.&3&\color{DarkBlue}{3}\end{array}&\\\color{Magenta}{9}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}3&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&7&\phantom{.}\\\hline\phantom{lll}&3&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&\phantom{.}\\\hline\phantom{lll}&&3&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&\phantom{.}&7\\\hline\phantom{lll}&&&&\color{DarkBlue}{3}&\color{DarkBlue}{0}\\&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&2&7\\\hline\phantom{lll}&&&&&3\end{array}&\begin{array}{c}\end{array}\end{array}$$$
As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{300}{9}=33. \overline{3}$$$
Answer: $$$\frac{300}{9}=33.\overline{3}$$$