# Fraction to Decimal Calculator

## Convert fractions to decimals step by step

The calculator will convert the given fraction (proper or improper) or mixed number into a decimal (possibly, repeating or recurring), with steps shown.

Enter a fraction or

If you don't need a mixed number, leave the left cell empty.
If you need a negative fraction, write the minus sign in the left cell.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

### Solution

Your input: convert $300\frac{200}{5}$ into a decimal.

Temporarily forget about the integer part, work with $\frac{200}{5}$

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{4}&\phantom{0}\end{array}&\\5&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}2&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $5$'s are in $2$? The answer is $0$.

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

Now, $2-0 \cdot 5 = 2 - 0= 2$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\color{GoldenRod}{0}&\phantom{4}&\phantom{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}\color{GoldenRod}{2}& 0 \downarrow&0\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}&2&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $5$'s are in $20$? The answer is $4$.

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

Now, $20-4 \cdot 5 = 20 - 20= 0$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}0&\color{Purple}{4}&\phantom{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}2&0& 0 \downarrow\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}&\color{Purple}{2}&\color{Purple}{0}\\-&\phantom{0}&\phantom{0}\\\phantom{lll}&2&0\\\hline\phantom{lll}&&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $5$'s are in $0$? The answer is $0$.

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

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

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}0&4&\color{DarkMagenta}{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}2&0&0\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}&2&0\\-&\phantom{0}&\phantom{0}\\\phantom{lll}&2&0\\\hline\phantom{lll}&&\color{DarkMagenta}{0}&\color{DarkMagenta}{0}\\&-&\phantom{0}&\phantom{0}\\\phantom{lll}&&&0\\\hline\phantom{lll}&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$

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

Therefore, $\frac{200}{5}=40$

Don't forget about the integer part: $300\frac{200}{5}=340$

Answer: $300\frac{200}{5}=340$