Fraction to Decimal Calculator

Your input: convert $\frac{1600}{22}$ into a decimal.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\22&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}1&6&0&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $22$'s are in $1$? The answer is $0$.

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

Now, $1-0 \cdot 22 = 1 - 0= 1$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}\color{Chocolate}{0}&\phantom{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}\color{Chocolate}{1}& 6 \downarrow&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $22$'s are in $16$? The answer is $0$.

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

Now, $16-0 \cdot 22 = 16 - 0= 16$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&\color{DarkCyan}{0}&\phantom{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6& 0 \downarrow&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}\color{DarkCyan}{1}&\color{DarkCyan}{6}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $22$'s are in $160$? The answer is $7$.

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

Now, $160-7 \cdot 22 = 160 - 154= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&\color{Chartreuse}{7}&\phantom{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6&0& 0 \downarrow&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}\color{Chartreuse}{1}&\color{Chartreuse}{6}&\color{Chartreuse}{0}&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $22$'s are in $60$? The answer is $2$.

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

Now, $60-2 \cdot 22 = 60 - 44= 16$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&7&\color{Brown}{2}&\phantom{.}&\phantom{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6&0&0&.& 0 \downarrow&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&\color{Brown}{6}&\color{Brown}{0}&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 5

How many $22$'s are in $160$? The answer is $7$.

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

Now, $160-7 \cdot 22 = 160 - 154= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&7&2&.&\color{Crimson}{7}&\phantom{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6&0&0&.&0& 0 \downarrow&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&4&\phantom{.}\\\hline\phantom{lll}&&\color{Crimson}{1}&\color{Crimson}{6}&\phantom{.}&\color{Crimson}{0}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 6

How many $22$'s are in $60$? The answer is $2$.

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

Now, $60-2 \cdot 22 = 60 - 44= 16$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&7&2&.&7&\color{Fuchsia}{2}&\phantom{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6&0&0&.&0&0& 0 \downarrow&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&\color{Fuchsia}{6}&\color{Fuchsia}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 7

How many $22$'s are in $160$? The answer is $7$.

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

Now, $160-7 \cdot 22 = 160 - 154= 6$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&7&2&.&7&2&\color{GoldenRod}{7}&\phantom{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6&0&0&.&0&0&0& 0 \downarrow&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&\color{GoldenRod}{1}&\color{GoldenRod}{6}&\color{GoldenRod}{0}\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&5&4\\\hline\phantom{lll}&&&&&&&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 8

How many $22$'s are in $60$? The answer is $2$.

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

Now, $60-2 \cdot 22 = 60 - 44= 16$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&7&2&.&7&2&7&\color{Violet}{2}&\phantom{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6&0&0&.&0&0&0&0& 0 \downarrow\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&5&4\\\hline\phantom{lll}&&&&&&&\color{Violet}{6}&\color{Violet}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&4&4\\\hline\phantom{lll}&&&&&&&1&6&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 9

How many $22$'s are in $160$? The answer is $7$.

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

Now, $160-7 \cdot 22 = 160 - 154= 6$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccccccccc}0&0&7&2&.&7&2&7&2&\color{DeepPink}{7}\end{array}&\\\color{Magenta}{22}&\phantom{-}\enclose{longdiv}{\begin{array}{cccccccccc}1&6&0&0&.&0&0&0&0&0\end{array}}&\\&\begin{array}{lllllllll}-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}0&\phantom{.}\\\hline\phantom{lll}1&6&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&0&\phantom{.}\\\hline\phantom{lll}1&6&0&\phantom{.}\\-&\phantom{6}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}1&5&4&\phantom{.}\\\hline\phantom{lll}&&6&0&\phantom{.}\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&4&4&\phantom{.}\\\hline\phantom{lll}&&1&6&\phantom{.}&0\\&-&\phantom{0}&\phantom{0}&\phantom{.}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&1&5&\phantom{.}&4\\\hline\phantom{lll}&&&&&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&4&4\\\hline\phantom{lll}&&&&&1&6&0\\&&&&-&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&1&5&4\\\hline\phantom{lll}&&&&&&&6&0\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&4&4\\\hline\phantom{lll}&&&&&&&\color{DeepPink}{1}&\color{DeepPink}{6}&\color{DeepPink}{0}\\&&&&&&-&\phantom{0}&\phantom{0}&\phantom{0}\\\phantom{lll}&&&&&&&1&5&4\\\hline\phantom{lll}&&&&&&&&&6\end{array}&\begin{array}{c}\end{array}\end{array}$

As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: $\frac{1600}{22}=72.7 \overline{27}$

Answer: $\frac{1600}{22}=72.7\overline{27}$