Calcolatrice da frazione a decimale

Your input: convert $$$\frac{3900}{45}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\45&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}3&9&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$45$$$'s are in $$$3$$$?

The answer is $$$0$$$.

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

Now, $$$3-45 \cdot 0 = 3 - 0= 3$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{DarkCyan}{0}&\phantom{0}&\phantom{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{DarkCyan}{3}& 9 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&9&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$45$$$'s are in $$$39$$$?

The answer is $$$0$$$.

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

Now, $$$39-45 \cdot 0 = 39 - 0= 39$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Blue}{0}&\phantom{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&9& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Blue}{3}&\color{Blue}{9}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$45$$$'s are in $$$390$$$?

The answer is $$$8$$$.

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

Now, $$$390-45 \cdot 8 = 390 - 360= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{Chocolate}{8}&\phantom{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&9&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{3}&\color{Chocolate}{9}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$45$$$'s are in $$$300$$$?

The answer is $$$6$$$.

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

Now, $$$300-45 \cdot 6 = 300 - 270= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&\color{Peru}{6}&\phantom{.}&\phantom{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&9&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&\color{Peru}{3}&\color{Peru}{0}&\color{Peru}{0}&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&0&\phantom{.}\\\hline\phantom{lll}&&3&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$45$$$'s are in $$$300$$$?

The answer is $$$6$$$.

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

Now, $$$300-45 \cdot 6 = 300 - 270= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&6&.&\color{DarkBlue}{6}&\phantom{6}&\phantom{6}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&9&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&0&\phantom{.}\\\hline\phantom{lll}&&\color{DarkBlue}{3}&\color{DarkBlue}{0}&\phantom{.}&\color{DarkBlue}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&7&\phantom{.}&0\\\hline\phantom{lll}&&&3&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$45$$$'s are in $$$300$$$?

The answer is $$$6$$$.

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

Now, $$$300-45 \cdot 6 = 300 - 270= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&6&.&6&\color{Red}{6}&\phantom{6}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&9&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&0&\phantom{.}\\\hline\phantom{lll}&&3&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&7&\phantom{.}&0\\\hline\phantom{lll}&&&\color{Red}{3}&\phantom{.}&\color{Red}{0}&\color{Red}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&7&0\\\hline\phantom{lll}&&&&&3&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$45$$$'s are in $$$300$$$?

The answer is $$$6$$$.

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

Now, $$$300-45 \cdot 6 = 300 - 270= 30$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&6&.&6&6&\color{DeepPink}{6}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&9&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&9&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&9&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\\-&\phantom{9}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&0&\phantom{.}\\\hline\phantom{lll}&&3&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&7&\phantom{.}&0\\\hline\phantom{lll}&&&3&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&7&0\\\hline\phantom{lll}&&&&&\color{DeepPink}{3}&\color{DeepPink}{0}&\color{DeepPink}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&2&7&0\\\hline\phantom{lll}&&&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{3900}{45}=86.6 \overline{6}$$$

Answer: $$$\frac{3900}{45}=86.6\overline{6}$$$