Calcolatrice da frazione a decimale

Your input: convert $$$\frac{900}{12}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\12&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$12$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-12 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{Fuchsia}{0}&\phantom{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{Fuchsia}{9}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$12$$$'s are in $$$90$$$?

The answer is $$$7$$$.

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

Now, $$$90-12 \cdot 7 = 90 - 84= 6$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{DarkCyan}{7}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{9}&\color{DarkCyan}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$12$$$'s are in $$$60$$$?

The answer is $$$5$$$.

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

Now, $$$60-12 \cdot 5 = 60 - 60= 0$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&7&\color{DarkMagenta}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&4&\phantom{.}\\\hline\phantom{lll}&\color{DarkMagenta}{6}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&6&0&\phantom{.}\\\hline\phantom{lll}&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$12$$$'s are in $$$0$$$?

The answer is $$$0$$$.

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

Now, $$$0-12 \cdot 0 = 0 - 0= 0$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&7&5&.&\color{Crimson}{0}\end{array}&\\\color{Magenta}{12}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}9&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}8&4&\phantom{.}\\\hline\phantom{lll}&6&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&6&0&\phantom{.}\\\hline\phantom{lll}&&\color{Crimson}{0}&\phantom{.}&\color{Crimson}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{900}{12}=75.0 \overline{}$$$

Answer: $$$\frac{900}{12}=75.0\overline{}$$$