Mathematicians, scientists, and economists commonly encounter very large and very small numbers. For example, Star Wars fans may remember Han Solo bragging about the *Millennium Falcon*‘s ability to make the Kessel Run in less than [latex]12[/latex] parsecs in Episode IV. He was referring to a smuggler’s route with sections that were flown in hyperspace, making length an important factor in how quickly a ship could make the run.

In reality, a parsec is a unit of length used to measure large distances to objects outside the solar system. A parsec is equal to about [latex]31[/latex] trillion kilometers or [latex]19[/latex] trillion miles in length. Rather than writing all the zeros associated with the number [latex]1[/latex] trillion [latex](1,000,000,000,000)[/latex], we commonly use the written words or scientific notation. Scientific notation uses exponents to represent the number of zeros that come before or after the important digits of a very small or large number. Using scientific notation, [latex]19[/latex] trillion miles would be written as [latex]{1.9}\times{10}^{13}[/latex] miles.

The most distant space probe, Voyager [latex]1[/latex], was [latex]0.0006[/latex] parsecs from Earth as of March [latex]2015[/latex]. It took Voyager [latex]37[/latex] years to cover that distance. Voyager 1 was launched by NASA on September [latex]5, 1977[/latex]. As of [latex]2013[/latex], the probe was moving with a relative velocity to the sun of about [latex]17030[/latex] m/s. With the velocity the probe is currently maintaining, Voyager [latex]1[/latex] is traveling about [latex]325[/latex] million miles per year, or [latex]520[/latex] million kilometers per year. Here are some more distances to well-known astronomical objects in parsecs:

- The distance to the open cluster Pleiades is [latex]130[/latex] parsecs from Earth. That’s [latex]{1.7}\times{10}^{15}[/latex] miles.
- The center of the Milky Way is more than [latex]8[/latex] kiloparsecs (a kiloparsec is [latex]1000[/latex] parsecs) from Earth, and the Milky Way is roughly [latex]34[/latex] kiloparsecs across.
- The nearest star to Earth, Proxima Centauri, is about [latex]1.3[/latex] parsecs from the sun.
- Most of the stars visible to the unaided eye in the nighttime sky are within [latex]500[/latex] parsecs of the sun.

In this module, you will learn the rules for algebraic operations on terms with exponents then apply them to calculations involving very large or small numbers.