Fraction to Decimal Calculator

Your input: convert $$$\frac{3500}{45}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\45&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}3&5&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$45$$$'s are in $$$3$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

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

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}\color{Fuchsia}{0}&\phantom{0}&\phantom{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}\color{Fuchsia}{3}& 5 \downarrow&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&5&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$45$$$'s are in $$$35$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$35-45 \cdot 0 = 35 - 0= 35$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&\color{Peru}{0}&\phantom{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&5& 0 \downarrow&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{Peru}{3}&\color{Peru}{5}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$45$$$'s are in $$$350$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$350-45 \cdot 7 = 350 - 315= 35$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&\color{DeepPink}{7}&\phantom{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&5&0& 0 \downarrow&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{3}&\color{DeepPink}{5}&\color{DeepPink}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&1&5&\phantom{.}\\\hline\phantom{lll}&3&5&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$45$$$'s are in $$$350$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$350-45 \cdot 7 = 350 - 315= 35$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&\color{Chocolate}{7}&\phantom{.}&\phantom{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&5&0&0&.& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&1&5&\phantom{.}\\\hline\phantom{lll}&\color{Chocolate}{3}&\color{Chocolate}{5}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&1&5&\phantom{.}\\\hline\phantom{lll}&&3&5&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$45$$$'s are in $$$350$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$350-45 \cdot 7 = 350 - 315= 35$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&7&.&\color{Chartreuse}{7}&\phantom{7}&\phantom{7}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&5&0&0&.&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&1&5&\phantom{.}\\\hline\phantom{lll}&3&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&1&5&\phantom{.}\\\hline\phantom{lll}&&\color{Chartreuse}{3}&\color{Chartreuse}{5}&\phantom{.}&\color{Chartreuse}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&1&\phantom{.}&5\\\hline\phantom{lll}&&&3&\phantom{.}&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$45$$$'s are in $$$350$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$350-45 \cdot 7 = 350 - 315= 35$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&7&.&7&\color{OrangeRed}{7}&\phantom{7}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&5&0&0&.&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&1&5&\phantom{.}\\\hline\phantom{lll}&3&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&1&5&\phantom{.}\\\hline\phantom{lll}&&3&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&1&\phantom{.}&5\\\hline\phantom{lll}&&&\color{OrangeRed}{3}&\phantom{.}&\color{OrangeRed}{5}&\color{OrangeRed}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&1&5\\\hline\phantom{lll}&&&&&3&5&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 7

How many $$$45$$$'s are in $$$350$$$?

The answer is $$$7$$$.

Write down $$$7$$$ in the upper part of the table.

Now, $$$350-45 \cdot 7 = 350 - 315= 35$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccc}0&0&7&7&.&7&7&\color{Red}{7}\end{array}&\\\color{Magenta}{45}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccc}3&5&0&0&.&0&0&0\end{array}}&\\&\begin{array}{lllllll}-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}3&5&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}3&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}3&1&5&\phantom{.}\\\hline\phantom{lll}&3&5&0&\phantom{.}\\-&\phantom{5}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&3&1&5&\phantom{.}\\\hline\phantom{lll}&&3&5&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&3&1&\phantom{.}&5\\\hline\phantom{lll}&&&3&\phantom{.}&5&0\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&3&\phantom{.}&1&5\\\hline\phantom{lll}&&&&&\color{Red}{3}&\color{Red}{5}&\color{Red}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&3&1&5\\\hline\phantom{lll}&&&&&&3&5\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{3500}{45}=77.7 \overline{7}$$$

Answer: $$$\frac{3500}{45}=77.7\overline{7}$$$