Fraction to Decimal Calculator

Your input: convert $$$\frac{8400}{90}$$$ into a decimal.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{9}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\90&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}8&4&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$90$$$'s are in $$$8$$$?

The answer is $$$0$$$.

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

Now, $$$8-90 \cdot 0 = 8 - 0= 8$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}\color{Peru}{0}&\phantom{0}&\phantom{9}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}\color{Peru}{8}& 4 \downarrow&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&4&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$90$$$'s are in $$$84$$$?

The answer is $$$0$$$.

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

Now, $$$84-90 \cdot 0 = 84 - 0= 84$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&\color{DeepPink}{0}&\phantom{9}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&4& 0 \downarrow&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DeepPink}{8}&\color{DeepPink}{4}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}8&4&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$90$$$'s are in $$$840$$$?

The answer is $$$9$$$.

Write down $$$9$$$ in the upper part of the table.

Now, $$$840-90 \cdot 9 = 840 - 810= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&\color{Chartreuse}{9}&\phantom{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&4&0& 0 \downarrow&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{8}&\color{Chartreuse}{4}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&1&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 4

How many $$$90$$$'s are in $$$300$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$300-90 \cdot 3 = 300 - 270= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&9&\color{GoldenRod}{3}&\phantom{.}&\phantom{3}&\phantom{3}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&4&0&0&.& 0 \downarrow&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}8&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&1&0&\phantom{.}\\\hline\phantom{lll}&\color{GoldenRod}{3}&\color{GoldenRod}{0}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&0&\phantom{.}\\\hline\phantom{lll}&&3&0&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 5

How many $$$90$$$'s are in $$$300$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$300-90 \cdot 3 = 300 - 270= 30$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&9&3&.&\color{Red}{3}&\phantom{3}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&4&0&0&.&0& 0 \downarrow\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}8&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&1&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&0&\phantom{.}\\\hline\phantom{lll}&&\color{Red}{3}&\color{Red}{0}&\phantom{.}&\color{Red}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&7&\phantom{.}&0\\\hline\phantom{lll}&&&3&\phantom{.}&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 6

How many $$$90$$$'s are in $$$300$$$?

The answer is $$$3$$$.

Write down $$$3$$$ in the upper part of the table.

Now, $$$300-90 \cdot 3 = 300 - 270= 30$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccccc}0&0&9&3&.&3&\color{OrangeRed}{3}\end{array}&\\\color{Magenta}{90}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccccc}8&4&0&0&.&0&0\end{array}}&\\&\begin{array}{llllll}-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}8&4&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}8&4&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}8&1&0&\phantom{.}\\\hline\phantom{lll}&3&0&0&\phantom{.}\\-&\phantom{4}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&2&7&0&\phantom{.}\\\hline\phantom{lll}&&3&0&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&2&7&\phantom{.}&0\\\hline\phantom{lll}&&&\color{OrangeRed}{3}&\phantom{.}&\color{OrangeRed}{0}&\color{OrangeRed}{0}\\&&-&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&2&\phantom{.}&7&0\\\hline\phantom{lll}&&&&&3&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $$$\frac{8400}{90}=93. \overline{3}$$$

Answer: $$$\frac{8400}{90}=93.\overline{3}$$$