what is the difference between 3db and 10 db attenuator when use in a application?

Answer 1

A 3 dB attenuator reduces a signal to 1/2 its original value. A 10 dB attenuator reduces a signal to 1/10 its original value.

If you follow the link below, the graph on the right of the screen shows the log nature of the dB scale.

Answer 2

Depends on whether you attenuate amplitute or power

From Wikipedia

http://en.wikipedia.org/wiki/Decibel

[edit] Examples
As examples, if PdB is 10 dB greater than PdB0, then P is ten times P0. If PdB is 3 dB greater, the power ratio is very close to a factor of two .