Fraction to Decimal Calculator

Your input: convert $\frac{1500}{24}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{6}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\24&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $24$'s are in $1$? The answer is $0$.

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

Now, $1-0 \cdot 24 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{6}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}\color{Fuchsia}{1}& 5 \downarrow&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $24$'s are in $15$? The answer is $0$.

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

Now, $15-0 \cdot 24 = 15 - 0= 15$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&\color{SaddleBrown}{0}&\phantom{6}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&5& 0 \downarrow&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{SaddleBrown}{1}&\color{SaddleBrown}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $24$'s are in $150$? The answer is $6$.

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

Now, $150-6 \cdot 24 = 150 - 144= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&\color{DarkBlue}{6}&\phantom{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&5&0& 0 \downarrow&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DarkBlue}{1}&\color{DarkBlue}{5}&\color{DarkBlue}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $24$'s are in $60$? The answer is $2$.

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

Now, $60-2 \cdot 24 = 60 - 48= 12$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&\color{Brown}{2}&\phantom{.}&\phantom{5}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&5&0&0&.& 0 \downarrow\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{6}&\color{Brown}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&4&8&\phantom{.}\\\hline\phantom{lll}&&1&2&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $24$'s are in $120$? The answer is $5$.

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

Now, $120-5 \cdot 24 = 120 - 120= 0$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccc}0&0&6&2&.&\color{Chocolate}{5}\end{array}&\\\color{Magenta}{24}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccc}1&5&0&0&.&0\end{array}}&\\&\begin{array}{lllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}1&4&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&4&8&\phantom{.}\\\hline\phantom{lll}&&\color{Chocolate}{1}&\color{Chocolate}{2}&\phantom{.}&\color{Chocolate}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&1&2&\phantom{.}&0\\\hline\phantom{lll}&&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{1500}{24}=62.5 \overline{}$

Answer: $\frac{1500}{24}=62.5\overline{}$