1. **State the problem:** Simplify the fraction $\frac{9999}{9999999999999}$.\n\n2. **Recall the formula:** Simplifying a fraction means dividing numerator and denominator by their greatest common divisor (GCD).\n\n3. **Find the GCD:** We need to find $\gcd(9999, 9999999999999)$.\n\n4. **Calculate GCD:** Notice that $9999 = 9,999$ and $9999999999999 = 9,999,999,999,999$. Both numbers end with 9s and are related to repunits.\n\n5. **Express numerator:** $9999 = 10^4 - 1$.\n\n6. **Express denominator:** $9999999999999 = 10^{13} - 1$.\n\n7. **Use property:** $\gcd(10^m - 1, 10^n - 1) = 10^{\gcd(m,n)} - 1$.\n\n8. **Calculate $\gcd(4,13)$:** Since 13 is prime and does not divide 4, $\gcd(4,13) = 1$.\n\n9. **Therefore,** $\gcd(9999, 9999999999999) = 10^1 - 1 = 9$.\n\n10. **Divide numerator and denominator by 9:**\n$$\frac{9999}{9999999999999} = \frac{9999 \div 9}{9999999999999 \div 9} = \frac{1111}{1111111111111}.$$\n\n11. **Final simplified fraction:** $\boxed{\frac{1111}{1111111111111}}$.