Calculatrice de conversion de fractions en décimales

Your input: convert $$$\frac{900}{27}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\27&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}9&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$27$$$'s are in $$$9$$$?

The answer is $$$0$$$.

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

Now, $$$9-27 \cdot 0 = 9 - 0= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{DarkBlue}{0}&\phantom{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{DarkBlue}{9}& 0 \downarrow&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{Chocolate}{3}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0& 0 \downarrow&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{9}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&9&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&3&\color{DarkMagenta}{3}&\phantom{.}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0&0&.& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&\color{DarkMagenta}{9}&\color{DarkMagenta}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&3&3&.&\color{Purple}{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0&0&.&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&&\color{Purple}{9}&\phantom{.}&\color{Purple}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&3&3&.&3&\color{BlueViolet}{3}&\phantom{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0&0&.&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&\color{BlueViolet}{9}&\color{BlueViolet}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&1\\\hline\phantom{lll}&&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&3&3&.&3&3&\color{Crimson}{3}&\phantom{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0&0&.&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&9&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&1\\\hline\phantom{lll}&&&&&\color{Crimson}{9}&\color{Crimson}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&3&3&.&3&3&3&\color{DarkCyan}{3}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0&0&.&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&9&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&1\\\hline\phantom{lll}&&&&&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&&\color{DarkCyan}{9}&\color{DarkCyan}{0}\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&8&1\\\hline\phantom{lll}&&&&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 8

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&3&3&.&3&3&3&3&\color{GoldenRod}{3}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0&0&.&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&9&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&1\\\hline\phantom{lll}&&&&&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&&9&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&8&1\\\hline\phantom{lll}&&&&&&&\color{GoldenRod}{9}&\color{GoldenRod}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&8&1\\\hline\phantom{lll}&&&&&&&&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 9

How many $$$27$$$'s are in $$$90$$$?

The answer is $$$3$$$.

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

Now, $$$90-27 \cdot 3 = 90 - 81= 9$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&3&3&.&3&3&3&3&3&\color{Chartreuse}{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}9&0&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}8&1&\phantom{.}\\\hline\phantom{lll}&9&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&&9&\phantom{.}&0\\&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&8&\phantom{.}&1\\\hline\phantom{lll}&&&&9&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&8&1\\\hline\phantom{lll}&&&&&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&&9&0\\&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&8&1\\\hline\phantom{lll}&&&&&&&9&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&8&1\\\hline\phantom{lll}&&&&&&&&\color{Chartreuse}{9}&\color{Chartreuse}{0}\\&&&&&&&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&8&1\\\hline\phantom{lll}&&&&&&&&&9\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{900}{27}=33. \overline{333}$$$

Answer: $$$\frac{900}{27}=33.\overline{333}$$$