Decibels are logarithmic, not linear. If the noise floor is 45 dB and you add another 45 dB from your speakers, the combined dB is 48. If you double the noise and add 90 dB to the ambient, the combined level is 90.00014. The numbers to the right of the decimal is the ambient contribution, which is essentially zero.
The formula for adding two decibels dB1 and dB2 is 10 x Log [10^(dB1/10) + 10^(dB2/10) ]