To determine the mass of an unknown gas sample with a density of 1.70 grams per liter and a volume of 120 milliliters, we start by converting the volume from milliliters to liters. Since 1 milliliter is equal to \(10^{-3}\) liters, we can convert 120 milliliters as follows:

\[120 \, \text{ml} = 120 \times 10^{-3} \, \text{liters} = 0.120 \, \text{liters}\]

Next, we apply the density formula, which relates mass, volume, and density:

\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]

Rearranging this formula to solve for mass gives us:

\[\text{Mass} = \text{Density} \times \text{Volume}\]

Substituting the known values into the equation:

\[\text{Mass} = 1.70 \, \text{grams/liter} \times 0.120 \, \text{liters} = 0.204 \, \text{grams}\]

When considering significant figures, the density (1.70 grams per liter) has three significant figures, while the volume (0.120 liters) has four. Therefore, the final answer should be reported with three significant figures, resulting in a mass of:

\[\text{Mass} = 0.204 \, \text{grams}\]

This calculation demonstrates how to effectively use density to find mass, ensuring proper unit conversions and adherence to significant figure rules.