Calcolatrice da frazione a decimale

Your input: convert $$$\frac{400}{30}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{1}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\30&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$30$$$'s are in $$$4$$$?

The answer is $$$0$$$.

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

Now, $$$4-30 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Crimson}{0}&\phantom{1}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Crimson}{4}& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$30$$$'s are in $$$40$$$?

The answer is $$$1$$$.

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

Now, $$$40-30 \cdot 1 = 40 - 30= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{DarkBlue}{1}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{4}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&1&\color{Green}{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&0&\phantom{.}\\\hline\phantom{lll}\color{Green}{1}&\color{Green}{0}&\color{Green}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&1&3&.&\color{Chartreuse}{3}&\phantom{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&0&\phantom{.}\\\hline\phantom{lll}&\color{Chartreuse}{1}&\color{Chartreuse}{0}&\phantom{.}&\color{Chartreuse}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&\phantom{.}&9&0\\\hline\phantom{lll}&&1&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$30$$$'s are in $$$100$$$?

The answer is $$$3$$$.

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

Now, $$$100-30 \cdot 3 = 100 - 90= 10$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&1&3&.&3&\color{Peru}{3}\end{array}&\\\color{Magenta}{30}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}4&0&0&.&0&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}3&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&9&0&\phantom{.}\\\hline\phantom{lll}&1&0&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&\phantom{.}&9&0\\\hline\phantom{lll}&&\color{Peru}{1}&\phantom{.}&\color{Peru}{0}&\color{Peru}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&9&\phantom{.}&0\\\hline\phantom{lll}&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{400}{30}=13. \overline{3}$$$

Answer: $$$\frac{400}{30}=13.\overline{3}$$$