The scientific “unit” we call the decibel

But dB is not a unit, it is a multiplier. dB on its own is unitless and if we say "X is reduced by 6 dB" you know that the value of X is half of what it was before (×0.5) if something is amplified by 6 dB it is double of what it was before (×2.0)¹

Note that the unit only starts to play a role when you reference your dB value to some absolute maximum, e.g.:

  dBV which is referenced to 1V RMS
  
  dBu which is referenced to 0.775V RMS (1mW into a typical audio system impedance of 600 Ohms)  
  
  dBFS which is referenced to a digital audio maximum level (0dBFS) beyond which your numeric range would clip (meaning all practical values will be negative) 
  
  dBSPL which is refrenced to the Sound Pressure Level that is at the lower edge of hearing (0 dBSPL), this is what people mean when they say the engine of a starting airplane is 120dB loud  
  

Now dB is extremely useful in all fields where your values span extremely big ranges, like in audio engineering, where the ratio between high and low values can easily have a ratio of 1:10 Millions. So unless you want people to count zeroes behind the comma, dB is the way to go.

When we think about the connection between analog and digital audio dB is useful because despite you having volts on the one side and bits on the other side a 6dB change on one side translates to a 6dB change on the other, the reference has just changed. If we had no dB we would have to do conversions constantly.

Going from multiplier x to dB: 20×log₁₀(x)

Going from dB to multiplier x: 10^(x/20)

If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)

But you can see, dB is just a way to describe a unreferenced size change in a uniform way or to describe a referenced ratio. And then it would be good to know what that reference is. So if someone says a thing has 40dB you they forgot to tell you the unit.

¹ this is true for the amplitude of a signal and differs when we talk about the power of a signal, where 3dB is a doubling/halving.

> > That said, I don’t know how to pronounce “3e5”

> "Three to the exponent of five." Or "Three Exponent Five." Or "Three Exp Five."

Somehow, you need to distinguish between 3^5 (=243), 3 x e^5 (=~445.24), and 3 x 10^5 (=300,000).

I'd pronounce "3e5" and "three times ten to the 5" in most cases.

> this is in the same tradition that prompted us to name the “wat” in honor of James Watt.

The unit is Watt, not Wat.

I'm sorry, that you missed the hilarious joke!

For reference: https://www.destroyallsoftware.com/talks/wat