Calculadora de frações para decimais

Your input: convert $\frac{1700}{34}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\34&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&7&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $34$'s are in $1$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $1-0 \cdot 34 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Red}{0}&\phantom{0}&\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{34}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Red}{1}& 7 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $34$'s are in $17$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $17-0 \cdot 34 = 17 - 0= 17$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{OrangeRed}{0}&\phantom{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{34}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{OrangeRed}{1}&\color{OrangeRed}{7}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $34$'s are in $170$? The answer is $5$.

Write down the calculated result in the upper part of the table.

Now, $170-5 \cdot 34 = 170 - 170= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Crimson}{5}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{34}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Crimson}{1}&\color{Crimson}{7}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&7&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $34$'s are in $0$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $0-0 \cdot 34 = 0 - 0= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&5&\color{BlueViolet}{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{34}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&7&0&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{0}&\color{BlueViolet}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $34$'s are in $0$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $0-0 \cdot 34 = 0 - 0= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&5&0&.&\color{SaddleBrown}{0}\end{array}&\\\color{Magenta}{34}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&7&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&7&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&7&0&\phantom{.}\\-&\phantom{7}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&7&0&\phantom{.}\\\hline\phantom{lll}&&0&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&0&\phantom{.}\\\hline\phantom{lll}&&&\color{SaddleBrown}{0}&\phantom{.}&\color{SaddleBrown}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{1700}{34}=50.0 \overline{}$

Answer: $\frac{1700}{34}=50.0\overline{}$