Fraction to Decimal Calculator

Your input: convert $\frac{1600}{25}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\25&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&6&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $25$'s are in $1$? The answer is $0$.

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

Now, $1-0 \cdot 25 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Purple}{0}&\phantom{0}&\phantom{6}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Purple}{1}& 6 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $25$'s are in $16$? The answer is $0$.

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

Now, $16-0 \cdot 25 = 16 - 0= 16$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{Peru}{0}&\phantom{6}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&6& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{1}&\color{Peru}{6}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $25$'s are in $160$? The answer is $6$.

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

Now, $160-6 \cdot 25 = 160 - 150= 10$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{Violet}{6}&\phantom{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&6&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{1}&\color{Violet}{6}&\color{Violet}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $25$'s are in $100$? The answer is $4$.

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

Now, $100-4 \cdot 25 = 100 - 100= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{OrangeRed}{4}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&6&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&5&0&\phantom{.}\\\hline\phantom{lll}&\color{OrangeRed}{1}&\color{OrangeRed}{0}&\color{OrangeRed}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&0&0&\phantom{.}\\\hline\phantom{lll}&&&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $25$'s are in $0$? The answer is $0$.

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

Now, $0-0 \cdot 25 = 0 - 0= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&4&.&\color{Chartreuse}{0}\end{array}&\\\color{Magenta}{25}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&6&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&5&0&\phantom{.}\\\hline\phantom{lll}&1&0&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&1&0&0&\phantom{.}\\\hline\phantom{lll}&&&\color{Chartreuse}{0}&\phantom{.}&\color{Chartreuse}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Since the remainder is $0$, then we are done.

Therefore, $\frac{1600}{25}=64.0$

Answer: $\frac{1600}{25}=64.0$