RC Lowpass cut off, single pole.

Fundamental question.

A single pole low pass filter, lets say: RC lowpass, will have a VERY shallow cut off.

A 5 pole filter will have a VERY STEEP cut off.

The question:
If I were to design a single pole low pass for 100Hz, due to the shallow cut off, it probably wouldn't actually cut off right at 100Hz correct?

It may actually pass 110, and even 120, etc..., correct?

Basically, the higher order, the higher accuracy...if I am understanding correctly?

Thanks

The "cut-off" frequency is where the amplitude decreases by 3db, AKA 50% power for a single pole filter. For a single pole filter the drop in frequency will be very shallow compared to a higher order filter. So yes your understanding is correct.

Wikipedia has normalized Bode plots for 1st through 5th order Butterworth lowpass filters. See the plot under The transfer function.