Page 50 - Master Handbook of Acoustics

p = (20 μPa)(12,589)
p = 251,785 μPa

There is another lesson here. The 82 has two significant figures. The 251,785 has six significant

figures and implies a precision that is not there. Just because a calculator says so doesn’t make it so.
A better answer is 252,000 μPa, or 0.252 Pa.

Logarithmic and Exponential Forms Compared

The logarithmic and exponential forms of numerical expression are equivalent as can be seen in
Table 2-1. When working with decibels, it is important that this equivalence be understood.
Let’s say we have a power ratio of 5:

There are two 10s in the exponential statement, but they come from different sources as indicated by
the arrows. Now let us treat a sound pressure ratio of 5:

Remember that sound-pressure level in air means that the reference pressure (p ) in the pressure
ref
ratio is 20 μPa. There are other reference quantities; some of the most common ones are listed in
Table 2-3. The prefixes of Table 2-4 are often employed when dealing with very small and very large
numbers. These prefixes are the Greek names for the power exponents of 10.