E.g. decibels (dB) is a ratio of identical quantities $q_1$ and $q_2$. So the ratio's unit will be:

$[\frac{q_1}{q_2}] = \frac{[q_1]}{[q_1]} = \frac{1 [whatever]}{1 [whatever]} = 1 = 0dB$

So the units are gone.

If you express the ratio in logrithmic terms, you need to be notified about it. That's what the non-SI unit dB is doing: !nota bene, I'm a logarithmic number!

This comes from telecommunications. dB is the newer term, indicating $lg$ has been used. Before, at the times of first telephones, Neper was used (Np) to express ratios by $ln$.

You are free to use ratios on an anything. E.g. you could say:

• my shoes are 10 % larger than yours
• which is a 1.1 ratio
• which is $+.83$ dB (I leave it up to you to discover the hidden square and 10)

E.g. decibels (dB) is a ratio of identical quantities $q_1$ and $q_2$. So the ratio's unit will be:

$[\frac{q_1}{q_2}] = \frac{[q_1]}{[q_1]} = \frac{1 [whatever]}{1 [whatever]} = 1 = 0dB$

So the units are gone.

If you express the ratio in logrithmic terms, you need to be notified about it. That's what the non-SI unit dB is doing: !nota bene, I'm a logarithmic number!

This comes from telecommunications. dB is the newer term, indicating $lg$ has been used. Before, at the times of first telephones, Neper was used (Np) to express ratios by $ln$.

You are free to use ratios on an anything. E.g. you could say:

• my shoes are 10 % larger than yours
• which is a 1.1 ratio
• which is $+.83$ dB (I leave it up to you to discover the hidden square and 10)

An important point: In physics the units denote both the phenomenon and its measurement, like:

• force F = m * a <=> 1 [kg m s^-2]
• mass m <=> 1 [kg]
• acceleration a <=> 1 [m s^-2]

This is also a unique error check when doing more complicated calculations, you won't find anywhere else. Whatever you calculated, units must still equal on both sides. If they don't: error. If they do: perhaps it's correct.