Angle Random Walk Noise - MEMS Gyro Error sources
As Brian Drummond mentions in comment above, the output of a gyroscope is rotation rate, not heading, so at 10 Hz sampling frequency, the noise should be (0.02 degrees/s/sqrt(Hz)) * sqrt(10 Hz). The frequency chosen here should be your sampling frequency. The final units of your noise should be in the same units the sensor is measuring.

To get the error for your dead reckoning, this noise then has to be integrated over time, which will leave you with units of degrees.