What is 0.3 repeating as a fraction in simplest form?

To convert the repeating decimal \(0.333...\) (where 3 repeats infinitely) into a fraction:

Step 1: Assign the repeating decimal to a variable.
Let \(x = 0.333...\).

Step 2: Multiply both sides of the equation by 10 to shift the decimal point.
\(10x = 3.333...\)

Step 3: Subtract the original equation (\(x = 0.333...\)) from this new equation.
\[
10x - x = 3.333... - 0.333...
\]
This simplifies to:
\[
9x = 3
\]

Step 4: Solve for \(x\).
\[
x = \frac{3}{9}
\]

Step 5: Simplify the fraction.
\[
\frac{3}{9} = \frac{1}{3}
\]

Thus, \(0.333...\) as a fraction in its simplest form is \(1/3\).