Fraction to Decimal Calculator

Your input: convert $\frac{3800}{45}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{8}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\45&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}3&8&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $45$'s are in $3$? The answer is $0$.

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

Now, $3-0 \cdot 45 = 3 - 0= 3$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Green}{0}&\phantom{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Green}{3}& 8 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&8&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $45$'s are in $38$? The answer is $0$.

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

Now, $38-0 \cdot 45 = 38 - 0= 38$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Violet}{0}&\phantom{8}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&8& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Violet}{3}&\color{Violet}{8}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&8&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $45$'s are in $380$? The answer is $8$.

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

Now, $380-8 \cdot 45 = 380 - 360= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{Brown}{8}&\phantom{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&8&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Brown}{3}&\color{Brown}{8}&\color{Brown}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $45$'s are in $200$? The answer is $4$.

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

Now, $200-4 \cdot 45 = 200 - 180= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&\color{Crimson}{4}&\phantom{.}&\phantom{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&8&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&\color{Crimson}{2}&\color{Crimson}{0}&\color{Crimson}{0}&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $45$'s are in $200$? The answer is $4$.

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

Now, $200-4 \cdot 45 = 200 - 180= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&4&.&\color{BlueViolet}{4}&\phantom{4}&\phantom{4}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&8&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&0&\phantom{.}\\\hline\phantom{lll}&&\color{BlueViolet}{2}&\color{BlueViolet}{0}&\phantom{.}&\color{BlueViolet}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&2&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $45$'s are in $200$? The answer is $4$.

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

Now, $200-4 \cdot 45 = 200 - 180= 20$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&4&.&4&\color{DarkMagenta}{4}&\phantom{4}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&8&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&\color{DarkMagenta}{2}&\phantom{.}&\color{DarkMagenta}{0}&\color{DarkMagenta}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&2&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 7

How many $45$'s are in $200$? The answer is $4$.

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

Now, $200-4 \cdot 45 = 200 - 180= 20$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&8&4&.&4&4&\color{Blue}{4}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&8&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&8&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&8&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&6&0&\phantom{.}\\\hline\phantom{lll}&2&0&0&\phantom{.}\\-&\phantom{8}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&0&\phantom{.}\\\hline\phantom{lll}&&2&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&8&\phantom{.}&0\\\hline\phantom{lll}&&&2&\phantom{.}&0&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&1&\phantom{.}&8&0\\\hline\phantom{lll}&&&&&\color{Blue}{2}&\color{Blue}{0}&\color{Blue}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&0\\\hline\phantom{lll}&&&&&&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{3800}{45}=84.4 \overline{4}$

Answer: $\frac{3800}{45}=84.4\overline{4}$