turning this into that

As scientists, we must constantly record, access, and manipulate data quantitatively. Measurements are numbers with specific units. It is very important to know exactly how to convert from one particular unit to another. We generally call this *"unit conversion"*.

There has been a decades long initiative to use the metric system in the sciences. For the most part, it has been successful, but there are still dozens and dozens of non-metric units commonly used today. A scientist must cope with the reality of real world units - whether they are metric or not.

English units have a great deal of history behind them and they are still in use today. We buy gasoline by the gallon, we post speed limits in mph (miles per hour), our barometric pressure is in inches of mercury. English units are not going away so we must be able to readily convert from English to metric and vice versa.

The metric system of units is a far more scientifically thought out system of units. The amounts all scale up and down by factors of ten. Common factors of ten are represented by metric prefixes. **You will need to memorize your metric prefixes for this course.** There is an entire section in Chapter 10 on metric prefixes. Not to mention the hundreds of web sites you can find listing them in various ways. I'm including the list for us in this class right here:

— from big to small —

prefix name | symbol | multiplier |
---|---|---|

tera- | T | × 10^{12} |

giga- | G | × 10^{9} |

mega- | M | × 10^{6} |

kilo- | k | × 10^{3} |

milli- | m | × 10^{-3} |

centi- | c | × 10^{-2} |

micro- | µ | × 10^{-6} |

nano- | n | × 10^{-9} |

pico- | p | × 10^{-12} |

Make sure you know these for your all your chemistry classes!

All students should learn the general method for converting units. The method is most commonly known as *dimensional analysis*. Other popular names that are directly rated are the *unit factor method* or the *factor-label method*. Units that represent the same measured quantity are written mathematically as a fraction (a relation). Because the two units match in describing the actual amount or physical quantity, the fraction is by definition a *unit fraction* meaning the equivalent of 1 (one). In mathematics you can multiply by one over and over and the number will never change (unitary law of multiplication). Each time a unit factor is multiplied, the old unit will cancel out and the new unit will take its place along with the correct numeric value.

In general you will be doing English → English conversions, Metric → Metric conversions, and English → Metric conversions.

Dallas is about 200 miles from Austin. How far is Dallas from Austin in centimeters?

**The method:** Instead of trying to find the one conversion factor we need (mi to cm), we will use 3 conversion factors that are far more common. We will first convert miles to feet. Then we will convert feet to inches. And finally, we will convert inches to centimeters. That is three unit factors to convert our 200 miles to centimeters. The math and unit cancellations are shown below.

\(\require{cancel} \newcommand\ccancel[2][black]{\color{#1}{\bcancel{\color{black}{#2}}}} \left({200\,\ccancel[red]{\rm mi}\over 1}\right) \left({5280\,\ccancel[green]{\rm ft}\over 1\,\ccancel[red]{\rm mi}}\right) \left({12\,\ccancel[blue]{\rm in}\over 1\,\ccancel[green]{\rm ft}}\right)\)\(\left({2.54\,{\rm cm}\over 1\,\ccancel[blue]{\rm in}}\right) = 3.22\times 10^7\,{\rm cm}\)

This is 32.2 million centimeters. Each of the units cancel out except for the last unit desired. This is the *unit factor method* for conversions and it is very useful for all kinds of scientific conversions.

There are SOOOO many examples of dimensional analysis on the internet. Type it in and see for yourself. Tons of YouTube videos, tons of sites. You have no excuse in saying you couldn't find help on this topic. I'd elaborate more on it myself, but why? Go out there and explore the tons and tons of examples that are there for you to learn this super important method of analytical problem solving. Dimensional analysis is awesome.

__external links__

Converting Units on WikiHow