Fast corresponds to 125 milliseconds up and down. The needle would be moving much faster if you use analog, showing you the varying noise levels quickly.
The Fast Time Weighting is usually used for measuring all the sound in your environment, which may vary widely over time. Therefore, you would need to report the range of noise fluctuations e.g. 58 to 64 dB (A). Fast is generally the chosen Time Weighting for noise measurements.