White just means that there is no correlation among the noise samples. This results in a flat power spectral density, hence the analogy with "white" light.
When you say that the amplitude of the white Gaussian noise is 0.1 with a signal amplitude of 1, I'm guessing you mean an SNR of 10.
Y = awgn(x,10,'measured','linear');
Otherwise, it really does not make sense to talk about the "amplitude" of WGN. You can basically say that most of the values are +/- 3 standard deviations, so if you set the standard deviation to 0.1/3, you would basically get a WGN sequence that varies from [-0.1, 0.1];
noise = 0.1/3*randn(size(t));
So you could do:
x = cos(2*pi*100*t)+0.1/3*randn(size(t));