Calcolatrice da frazione a decimale

Your input: convert $$$\frac{1100}{15}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\15&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&1&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$15$$$'s are in $$$1$$$?

The answer is $$$0$$$.

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

Now, $$$1-15 \cdot 0 = 1 - 0= 1$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{7}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Fuchsia}{1}& 1 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$15$$$'s are in $$$11$$$?

The answer is $$$0$$$.

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

Now, $$$11-15 \cdot 0 = 11 - 0= 11$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{DarkCyan}{0}&\phantom{7}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&1& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{1}&\color{DarkCyan}{1}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$15$$$'s are in $$$110$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$110-15 \cdot 7 = 110 - 105= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{DarkMagenta}{7}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&1&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkMagenta}{1}&\color{DarkMagenta}{1}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$15$$$'s are in $$$50$$$?

The answer is $$$3$$$.

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

Now, $$$50-15 \cdot 3 = 50 - 45= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&\color{Crimson}{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&1&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&\phantom{.}\\\hline\phantom{lll}&&\color{Crimson}{5}&\color{Crimson}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&5&\phantom{.}\\\hline\phantom{lll}&&&5&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$15$$$'s are in $$$50$$$?

The answer is $$$3$$$.

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

Now, $$$50-15 \cdot 3 = 50 - 45= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&3&.&\color{Peru}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&1&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&5&\phantom{.}\\\hline\phantom{lll}&&&\color{Peru}{5}&\phantom{.}&\color{Peru}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&5\\\hline\phantom{lll}&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$15$$$'s are in $$$50$$$?

The answer is $$$3$$$.

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

Now, $$$50-15 \cdot 3 = 50 - 45= 5$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&3&.&3&\color{OrangeRed}{3}&\phantom{3}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&1&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&5&\phantom{.}\\\hline\phantom{lll}&&&5&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&5\\\hline\phantom{lll}&&&&&\color{OrangeRed}{5}&\color{OrangeRed}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&5\\\hline\phantom{lll}&&&&&&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$15$$$'s are in $$$50$$$?

The answer is $$$3$$$.

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

Now, $$$50-15 \cdot 3 = 50 - 45= 5$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&3&.&3&3&\color{Violet}{3}\end{array}&\\\color{Magenta}{15}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}1&1&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&1&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&1&0&\phantom{.}\\-&\phantom{1}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}1&0&5&\phantom{.}\\\hline\phantom{lll}&&5&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&5&\phantom{.}\\\hline\phantom{lll}&&&5&\phantom{.}&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&4&\phantom{.}&5\\\hline\phantom{lll}&&&&&5&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&5\\\hline\phantom{lll}&&&&&&\color{Violet}{5}&\color{Violet}{0}\\&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&4&5\\\hline\phantom{lll}&&&&&&&5\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{1100}{15}=73.3 \overline{3}$$$

Answer: $$$\frac{1100}{15}=73.3\overline{3}$$$