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

Related Note: Converting Fractions to Decimals