dB

A log ratio between signals. Typically the ratio between input and outputs in an electronic system.
The deciBell is 1/10th of a Bell, and used in the early Bell telephone systems as a measurement of power.

dB = 20 log (ratio of signals)

Example
For a gain of 10:1 in a system
dB = 20 log(10/1),   = 20 log 10
     = 20 x 1 [log of 10 is 1]
     = 20 dB
Therfore working the other way
40dB = 102
        = 100:1

Some common values
-80dB = 1080/20  = 10 000:1 
-6db =  10 -6/20  = 0.50118  ≈ 0.5
+6dB = 10 6/20  = 1.99526  ≈ 2.0
+1dB = 10 1/20  ≈ 1.12
+0.1dB ≈ 1.01 OR 1%