Fraction to Decimal Calculator

Your input: convert $\frac{100}{27}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{3}&\phantom{.}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}\end{array}&\\27&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}1&0&0\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $27$'s are in $1$? The answer is $0$.

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

Now, $1-0 \cdot 27 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{DarkMagenta}{0}&\phantom{0}&\phantom{3}&\phantom{.}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{DarkMagenta}{1}& 0 \downarrow&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $27$'s are in $10$? The answer is $0$.

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

Now, $10-0 \cdot 27 = 10 - 0= 10$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{GoldenRod}{0}&\phantom{3}&\phantom{.}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0& 0 \downarrow&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{GoldenRod}{1}&\color{GoldenRod}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $27$'s are in $100$? The answer is $3$.

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

Now, $100-3 \cdot 27 = 100 - 81= 19$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&\color{Chocolate}{3}&\phantom{.}&\phantom{7}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&.& 0 \downarrow&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chocolate}{1}&\color{Chocolate}{0}&\color{Chocolate}{0}&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $27$'s are in $190$? The answer is $7$.

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

Now, $190-7 \cdot 27 = 190 - 189= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&3&.&\color{OrangeRed}{7}&\phantom{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&.&0& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&\color{OrangeRed}{1}&\color{OrangeRed}{9}&\phantom{.}&\color{OrangeRed}{0}\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&9\\\hline\phantom{lll}&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $27$'s are in $10$? The answer is $0$.

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

Now, $10-0 \cdot 27 = 10 - 0= 10$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&3&.&7&\color{Violet}{0}&\phantom{3}&\phantom{7}&\phantom{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&.&0&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&9\\\hline\phantom{lll}&&&&\color{Violet}{1}&\color{Violet}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $27$'s are in $100$? The answer is $3$.

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

Now, $100-3 \cdot 27 = 100 - 81= 19$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&3&.&7&0&\color{DeepPink}{3}&\phantom{7}&\phantom{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&.&0&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&9\\\hline\phantom{lll}&&&&1&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&\color{DeepPink}{1}&\color{DeepPink}{0}&\color{DeepPink}{0}\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&1&9&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 7

How many $27$'s are in $190$? The answer is $7$.

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

Now, $190-7 \cdot 27 = 190 - 189= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&3&.&7&0&3&\color{Chartreuse}{7}&\phantom{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&.&0&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&9\\\hline\phantom{lll}&&&&1&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&1&0&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&\color{Chartreuse}{1}&\color{Chartreuse}{9}&\color{Chartreuse}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&1&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 8

How many $27$'s are in $10$? The answer is $0$.

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

Now, $10-0 \cdot 27 = 10 - 0= 10$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&3&.&7&0&3&7&\color{Fuchsia}{0}&\phantom{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&.&0&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&9\\\hline\phantom{lll}&&&&1&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&1&0&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&1&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&\color{Fuchsia}{1}&\color{Fuchsia}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&0\\\hline\phantom{lll}&&&&&&&1&0&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 9

How many $27$'s are in $100$? The answer is $3$.

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

Now, $100-3 \cdot 27 = 100 - 81= 19$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&3&.&7&0&3&7&0&\color{Crimson}{3}\end{array}&\\\color{Magenta}{27}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&0&0&.&0&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&0&0&\phantom{.}\\-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&8&1&\phantom{.}\\\hline\phantom{lll}&1&9&\phantom{.}&0\\-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&1&8&\phantom{.}&9\\\hline\phantom{lll}&&&&1&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&0\\\hline\phantom{lll}&&&&1&0&0\\&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&8&1\\\hline\phantom{lll}&&&&&1&9&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&8&9\\\hline\phantom{lll}&&&&&&&1&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&0\\\hline\phantom{lll}&&&&&&&\color{Crimson}{1}&\color{Crimson}{0}&\color{Crimson}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&&8&1\\\hline\phantom{lll}&&&&&&&&1&9\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{100}{27}=3. \overline{703}$

Answer: $\frac{100}{27}=3.\overline{703}$