Unit Analysis

Implications

Physics can often become confusing becausephysical quantities are often expressed in terms of different units. Forexample the speed of light is

c=186000 Mps=299000000 m/s=1light-second/second

c = 186000 英里/秒 = 299000000/= 1光秒/

Understanding the meaning of units isimportant for two reasons: it allows us to determine the dimensions of physicalquantities, and to understand the scale of physical phenomena.

In physics, the number associated with a physical quantity is meaningless unless the units are specified.

Units are not only useful in understanding the scale of a physical quantity, but also in determining its dimensions.

Scientific Notation

Because we will constantly encounter numbers, we want to be able to express them in the most concise way possible. It is quite cumbersome to write a small number as: 0.000000000001. How many zeros are there? You would have to count them all. Is this number smaller or greater than: 0.0000000000001?

We can instead use powers of 10 to express any number as a product of a digit term and an exponential term. For example,

Because we can also compress subunitary numbers: . This notation is not only more concise, but also much faster and error-proof in manipulations. For example:

Unit Prefixes

Tera$T$${10}^{12}$
Giga$G$${10}^{9}$
Mega$M$${10}^{6}$
Kilo$k$${10}^{3}$

${10}^{0}$$1$
Mili$m$${10}^{-3}$$0.001$
Micro$\mu$${10}^{-6}$
Nano$n$${10}^{-9}$
Pico$p$${10}^{-12}$