Fraction to Decimal Calculator

Your input: convert $\frac{700}{28}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\28&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}7&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $28$'s are in $7$? The answer is $0$.

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

Now, $7-0 \cdot 28 = 7 - 0= 7$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}\color{OrangeRed}{0}&\phantom{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{28}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{OrangeRed}{7}& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $28$'s are in $70$? The answer is $2$.

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

Now, $70-2 \cdot 28 = 70 - 56= 14$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&\color{GoldenRod}{2}&\phantom{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{28}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}7&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{7}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}5&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $28$'s are in $140$? The answer is $5$.

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

Now, $140-5 \cdot 28 = 140 - 140= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&2&\color{Brown}{5}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{28}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}7&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}5&6&\phantom{.}\\\hline\phantom{lll}\color{Brown}{1}&\color{Brown}{4}&\color{Brown}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&\phantom{.}\\\hline\phantom{lll}&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $28$'s are in $0$? The answer is $0$.

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

Now, $0-0 \cdot 28 = 0 - 0= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&2&5&.&\color{Violet}{0}\end{array}&\\\color{Magenta}{28}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}7&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}7&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}5&6&\phantom{.}\\\hline\phantom{lll}1&4&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&0&\phantom{.}\\\hline\phantom{lll}&&\color{Violet}{0}&\phantom{.}&\color{Violet}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{700}{28}=25.0 \overline{}$

Answer: $\frac{700}{28}=25.0\overline{}$