1. The problem is to convert 34 kilometers (km) to miles (mi) and express the answer as a mixed number in simplest form. 2. The conversion formula is: $$1 \text{ km} = 0.621371 \text{ mi}$$ 3. Multiply 34 km by the conversion factor to get miles: $$34 \times 0.621371 = 21.136614$$ 4. Now, convert the decimal 21.136614 to a mixed number. The whole number part is 21. 5. To convert the decimal part 0.136614 to a fraction, approximate it as $$\frac{136614}{1000000}$$. 6. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 136614 and 1000000 is 2: $$\frac{\cancel{136614}68107}{\cancel{1000000}500000}$$ 7. Approximate the fraction $$\frac{68107}{500000}$$ which is close to $$\frac{1}{7}$$ (since $$\frac{1}{7} \approx 0.142857$$). 8. Therefore, the mixed number is approximately $$21 \frac{1}{7}$$ miles. 9. Final answer: $$34 \text{ km} = 21 \frac{1}{7} \text{ mi}$$