Calcolatrice da frazione a decimale

Your input: convert $$$\frac{1300}{24}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{5}&\phantom{4}&\phantom{.}&\phantom{1}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\24&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&3&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$24$$$'s are in $$$1$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$1-24 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{Red}{0}&\phantom{0}&\phantom{5}&\phantom{4}&\phantom{.}&\phantom{1}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{Red}{1}& 3 \downarrow&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$24$$$'s are in $$$13$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$13-24 \cdot 0 = 13 - 0= 13$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{Blue}{0}&\phantom{5}&\phantom{4}&\phantom{.}&\phantom{1}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{1}&\color{Blue}{3}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$24$$$'s are in $$$130$$$?

The answer is $$$5$$$.

Write down $$$5$$$ in the upper part of the table.

Now, $$$130-24 \cdot 5 = 130 - 120= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&\color{DeepPink}{5}&\phantom{4}&\phantom{.}&\phantom{1}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{1}&\color{DeepPink}{3}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$24$$$'s are in $$$100$$$?

The answer is $$$4$$$.

Write down $$$4$$$ in the upper part of the table.

Now, $$$100-24 \cdot 4 = 100 - 96= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&\color{Crimson}{4}&\phantom{.}&\phantom{1}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&\color{Crimson}{1}&\color{Crimson}{0}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$24$$$'s are in $$$40$$$?

The answer is $$$1$$$.

Write down $$$1$$$ in the upper part of the table.

Now, $$$40-24 \cdot 1 = 40 - 24= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&4&.&\color{Violet}{1}&\phantom{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&6&\phantom{.}\\\hline\phantom{lll}&&&\color{Violet}{4}&\phantom{.}&\color{Violet}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&4&.&1&\color{DarkCyan}{6}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&4\\\hline\phantom{lll}&&&\color{DarkCyan}{1}&\phantom{.}&\color{DarkCyan}{6}&\color{DarkCyan}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&4&.&1&6&\color{DarkMagenta}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&\color{DarkMagenta}{1}&\color{DarkMagenta}{6}&\color{DarkMagenta}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&4&.&1&6&6&\color{DarkBlue}{6}&\phantom{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&\color{DarkBlue}{1}&\color{DarkBlue}{6}&\color{DarkBlue}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&4&4\\\hline\phantom{lll}&&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$24$$$'s are in $$$160$$$?

The answer is $$$6$$$.

Write down $$$6$$$ in the upper part of the table.

Now, $$$160-24 \cdot 6 = 160 - 144= 16$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&5&4&.&1&6&6&6&\color{Green}{6}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&3&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&3&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&3&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&2&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{3}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&9&6&\phantom{.}\\\hline\phantom{lll}&&&4&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&4\\\hline\phantom{lll}&&&1&\phantom{.}&6&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&4&4\\\hline\phantom{lll}&&&&&&1&6&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&1&4&4\\\hline\phantom{lll}&&&&&&&\color{Green}{1}&\color{Green}{6}&\color{Green}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&4&4\\\hline\phantom{lll}&&&&&&&&1&6\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1300}{24}=54.166 \overline{6}$$$

Answer: $$$\frac{1300}{24}=54.166\overline{6}$$$