What is the numerical ratio that is equivalent to 19.2 dB?

Answer: 83.17

Explanation:

By definition, the dB is an adimensional unit, used to simplify calculations when numbers are either too big or too small, specially in telecommunications.

It applies specifically to power, and it is defined as follows:

P (dB) = 10 log₁₀ P₁ / P₂

Usually P₂ is a reference, for instance, if P₂ = 1 mW, dB is called as dBm (dB referred to 1 mW), but it is always adimensional.

In our question, we know that we have a numerical ratio, that is expressed in dB as 19.2 dB.

Applying the dB definition, we can write the following:

10 log₁₀ X = 19.2 ⇒ log₁₀ X = 19.2 / 10 = 1.92

Solving the logarithmic equation, we can compute X as follows:

X = 10^1.92 = 83.17

X = 83.17