The uncertainty in momentum ($\Delta p$) is related to the uncertainty in velocity ($\Delta v$) and mass ($m$) by the definition of momentum: $\Delta p = m \cdot \Delta v$.

1. Identify Given Values: Uncertainty in momentum ($\Delta p$) = $1 \times 10^{-18} \text{ g cm s}^{-1}$ Mass of electron ($m$) = $9 \times 10^{-28} \text{ g}$

2. Calculation: Rearranging the formula to solve for $\Delta v$: $\Delta v = \frac{\Delta p}{m}$ $\Delta v = \frac{1 \times 10^{-18}}{9 \times 10^{-28}}$ $\Delta v = \frac{1}{9} \times 10^{10} \text{ cm s}^{-1}$ $\Delta v \approx 0.111 \times 10^{10} \text{ cm s}^{-1}$ $\Delta v \approx 1.11 \times 10^9 \text{ cm s}^{-1}$

Rounding to the nearest integer coefficient as per the options, the value is $1 \times 10^9 \text{ cm s}^{-1}$.