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.
Solution
Your input: convert 2005 into a decimal.
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{GoldenRod}{0}&\phantom{4}&\phantom{0}&\phantom{.}&\phantom{0}\end{array}&\\\color{Magenta}{5}&\phantom{-}\enclose{longdiv}{\begin{array}{ccccc}\color{GoldenRod}{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{DarkCyan}{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{DarkCyan}{2}&\color{DarkCyan}{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{Blue}{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{Blue}{0}&\color{Blue}{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{DarkBlue}{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{DarkBlue}{0}&\phantom{.}&\color{DarkBlue}{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
Answer: \frac{200}{5}=40.0