Why do we use decibel ratios like dB and dBm scales while calculating RF signal measurements using VNA or Spectrum Analyzers?

Because it is used to measure signal to noise ratio (SNR). It measures logarithmic unit and absolute unit. For example, Signal to noise ratio is

SNR=dB = log (P1/P2)  and dBm=log (P/1mW).

Thus, dB is used to quantify ratio between two intensity or power values while dBm is used to express an absolute value of power. Also dB is a dimensionless unit while dBm is an absolute unit.

During RF installation there tends to be Gain or Attenuation, therefore in calculating the RF signal, decibel (dB) values are used because it is easy to get the sum total Gain and Attenuation decibel values than multiplying the individual factors

Because it being logarithmic unit ,its easy to do mathematical summations, Simplification of complex calculations.

Because db is a logarithm nature,  easy way to find ratio of various signal

Decibel is used in RF measurements because it can represent very high numbers and very low numbers that are positive, that is usually hard to deal with it like it is, by manageable numbers.  

For example:  

500000 watt  is  10 Log ( 500000 ) = 56.9 dB 

0.0000001 watt is 10 Log (0.0000001) = -70 dB

Another benefit: it is relatively easy to do mathematical operations using dB. Multiplication and division are converted into Addition and Subtraction respectively. 

For example:

If we want the half of the number 500000 which is 250000. In order to get that result, we multiply 500000 by 1/2. On the other hand, to get the half of 56.9 dB we need jest to add -3 dB to 56.9 dB to get 53.9 dB ( 250000 in relative value). 

Hope that answers that question. 

Mainly there are two reasons to use dB on RF measurement than original measures. First, mathematical operations are easier when you do it on dB. Mutltiplication and division is converted into basic addition and substraction operations. This makes RF engineers life easier.Second, RF measurement are usually expressed in extremely low units such as milliwats and it would be easier to sense their values when converted to dBs. As an example an increase in power level from 3dbm to 6 dBm means the same as double the power (3 dB difference) which is a considerable difference.If you compare this to real power value measurements you might feel the difference. The previous numbers are equivalent to an increase of power from  0.002 to 0.004 watts.

Hope that helps.

To measure the signal amplitude , Frequency and Power level

Sound is a logrithimic quantity because of irregular shape of ears.

So it measure in same

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To be honest, I do not know, but I have had such a question for a long time, to which I have been trying to find an answer for a long time and it seems to me that you can help me find an answer to it. I heard that on the decibel meter app website you can download a phone application that would measure sound. How effective do you think it can be?

The Purpose of using decibel scale is to make a non linear system linear. Natural waves are Logarithmic in nature, So, while measuring their physical properties like pressure level or power we consider a reference point with which we measure its properties.