1. The problem is to understand the number 3.25434343... which appears to be a decimal with a repeating pattern. 2. Identify the repeating part: here, the digits "43" repeat indefinitely after the initial "3.25". 3. To express this number as a fraction, let $x = 3.25434343...$. 4. Multiply $x$ by 100 to shift the decimal two places right, aligning the repeating parts: $$100x = 325.434343...$$ 5. Multiply $x$ by 10000 to shift the decimal four places right, aligning the repeating parts further: $$10000x = 32543.434343...$$ 6. Subtract the equation from step 4 from the equation in step 5 to eliminate the repeating decimal: $$10000x - 100x = 32543.434343... - 325.434343...$$ $$9900x = 32218$$ 7. Solve for $x$: $$x = \frac{32218}{9900}$$ 8. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 32218 and 9900 is 2: $$x = \frac{\cancel{2}16109}{\cancel{2}4950}$$ 9. So, the simplified fraction is: $$x = \frac{16109}{4950}$$ 10. Therefore, the decimal 3.25434343... equals the fraction $\frac{16109}{4950}$.