exponent

Examples of exponent in the following topics:

• A Practical Aside - Orders of Magnitude

  • The order of magnitude estimate combines the lack of rigor of dimensional analysis with the lack of accuracy of keeping track of only the exponents; this makes multiplication in your head easier!
  • The first part of the tool is the knowledge of the various constants of nature in c.g.s units but you only need to keep the exponent in your head.

• Scientific Notation

  • In scientific notation all numbers are written in the form of $a\cdot 10^{b}$  ($a$ multiplied by ten raised to the power of $b$), where the exponent $b$ is an integer, and the coefficient $a$ is any real number.
  • Negative exponents are used for small numbers:
  • There are three parts to writing a number in scientific notation: the coefficient, the base, and the exponent.

• Damped transient motion

  • But now only the minus sign in the exponent makes sense, since otherwise the amplitude of the motion would increase with time.

• Some Basic Theorems for the Fourier Transform

  • This probably the best argument for using $f$ instead of $\omega$ since then the $2 \pi$ s are in the exponent and the problem goes away.

• Order of Magnitude Calculations

  • In its most common usage, the amount scaled is 10, and the scale is the exponent applied to this amount (therefore, to be an order of magnitude greater is to be 10 times, or 10 to the power of 1, greater).

• B.11 Chapter 11

  • Furthermore, the adiabatic exponent is given by $\gamma=\partial \ln p/\partial \ln \rho=(\rho/p) c_s^2

• Statistical Mechanics

  • The number density of photons can be determined in a similar way but the exponent in the integral is "2" instead of "3" yielding