To convert the repeating decimal \( 0.737373...\) to a fraction, we can use a common algebraic method.
Let: \[ x = 0.737373...\ \text{(This is our repeating decimal)} \]
Since the two digits "73" repeat, we can multiply \( x \) by 100 (which shifts the decimal point two places to the right): \[ 100x = 73.737373... \]
Next, we can set up an equation using these two expressions for \( x \): \[ 100x = 73.737373...\ \] \[ x = 0.737373... \]
Now, we subtract the second equation from the first: \[ 100x - x = 73.737373... - 0.737373... \] This results in: \[ 99x = 73 \]
To solve for \( x \), we divide both sides by 99: \[ x = \frac{73}{99} \]
Now, we need to check if \(\frac{73}{99}\) can be simplified. The greatest common divisor (GCD) of 73 and 99 is 1, since 73 is a prime number and does not divide 99.
Thus, the fraction \(\frac{73}{99}\) is already in its simplest form.
Therefore, the repeating decimal \( 0.737373...\) converted to a fraction in simplest form is: \[ \boxed{\frac{73}{99}} \]