Fraction to Decimal Calculator

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:

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

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.

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

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.

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

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

Bring down the next digit of the dividend.

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

Step 4

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

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

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

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccccc}0&4&0&.&\color{DeepPink}{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}2&0&0&.&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}2&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}\\\phantom{lll}2&0&\phantom{.}\\\hline\phantom{lll}&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&0&\phantom{.}\\\hline\phantom{lll}&&\color{DeepPink}{0}&\phantom{.}&\color{DeepPink}{0}\\&-&\phantom{0}&\phantom{.}&\phantom{0}\\\phantom{lll}&&&\phantom{.}&0\\\hline\phantom{lll}&&&&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

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

Therefore, $$$\frac{200}{5}=40.0$$$

Don't forget about the integer part: $$$300\frac{200}{5}=340.0$$$

Answer: $$$300\frac{200}{5}=340.0$$$