An absorption measurement with a $1$ cm path length yields a reading of $0\mathrm{.}002$ absorbance units with a noise of $0\mathrm{.}0005$ absorbance units and a mean noise reading of $0$ for $5$ scans averaged together. Assuming the noise for a single scan does not change if the path length is increased to $5$ cm and the number of scans is increase to $65,$ what is the signal to noise of the new measurement. Remember signal averaging form the previous module.