Calcolatrice da frazione a decimale

Your input: convert $$$\frac{8500}{3}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{2}&\phantom{8}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\3&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}8&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$3$$$'s are in $$$8$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$8-3 \cdot 2 = 8 - 6= 2$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{DarkBlue}{2}&\phantom{8}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{DarkBlue}{8}& 5 \downarrow&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}2&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$3$$$'s are in $$$25$$$?

The answer is $$$8$$$.

Write down $$$8$$$ in the upper part of the table.

Now, $$$25-3 \cdot 8 = 25 - 24= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}2&\color{Chocolate}{8}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&5& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{2}&\color{Chocolate}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}2&8&\color{DarkMagenta}{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&5&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}2&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}&\color{DarkMagenta}{1}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}2&8&3&\color{Purple}{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&5&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}2&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{1}&\color{Purple}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}2&8&3&3&.&\color{BlueViolet}{3}&\phantom{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&5&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}2&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&9&\phantom{.}\\\hline\phantom{lll}&&&\color{BlueViolet}{1}&\phantom{.}&\color{BlueViolet}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&9\\\hline\phantom{lll}&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$3$$$'s are in $$$10$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$10-3 \cdot 3 = 10 - 9= 1$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}2&8&3&3&.&3&\color{Crimson}{3}\end{array}&\\\color{Magenta}{3}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&5&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}6&\phantom{.}\\\hline\phantom{lll}2&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}2&4&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&\phantom{.}\\\hline\phantom{lll}&&1&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&9&\phantom{.}\\\hline\phantom{lll}&&&1&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&9\\\hline\phantom{lll}&&&&&\color{Crimson}{1}&\color{Crimson}{0}\\&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&9\\\hline\phantom{lll}&&&&&&1\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{8500}{3}=2833. \overline{3}$$$

Answer: $$$\frac{8500}{3}=2833.\overline{3}$$$