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 $$$\frac{1400}{35}$$$ into a decimal.
Write the problem in the special format:
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\35&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&4&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 1
How many $$$35$$$'s are in $$$1$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$1-35 \cdot 0 = 1 - 0= 1$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Blue}{0}&\phantom{0}&\phantom{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Blue}{1}& 4 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 2
How many $$$35$$$'s are in $$$14$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$14-35 \cdot 0 = 14 - 0= 14$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Fuchsia}{0}&\phantom{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&4& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Fuchsia}{1}&\color{Fuchsia}{4}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 3
How many $$$35$$$'s are in $$$140$$$?
The answer is $$$4$$$.
Write down $$$4$$$ in the upper part of the table.
Now, $$$140-35 \cdot 4 = 140 - 140= 0$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{OrangeRed}{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&4&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{1}&\color{OrangeRed}{4}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 4
How many $$$35$$$'s are in $$$0$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$0-35 \cdot 0 = 0 - 0= 0$$$.
Bring down the next digit of the dividend.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&\color{Purple}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&4&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{0}&\color{Purple}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
Step 5
How many $$$35$$$'s are in $$$0$$$?
The answer is $$$0$$$.
Write down $$$0$$$ in the upper part of the table.
Now, $$$0-35 \cdot 0 = 0 - 0= 0$$$.
$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&4&0&.&\color{Chocolate}{0}\end{array}&\\\color{Magenta}{35}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&4&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Chocolate}{0}&\phantom{.}&\color{Chocolate}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$
As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1400}{35}=40.0 \overline{}$$$
Answer: $$$\frac{1400}{35}=40.0\overline{}$$$