Section 1.3: Standards and Units

Not much for me to add here. This is basically a discussion of the fundamentality of length, mass, and time. They do put forth a fun term – “operational definition,” meaning a physical quantity that can be defined only by describing how it’s measured.

The one thing I’ll add that was useful for me to understand is this: When it comes to units and scientific notation, remember you’re basically dealing with a base-3 system.

Thousand = something*10^3

Million = something*10^(3+3)

Billion = something*10^(3+3+3)

Trillion = something*10^(3+3+3+3)

It’s probably an obvious insight, but it sped up my ability to parse numbers quickly, which is crucial for problems with a lot of variables to hold in your head. I think it’s useful for students to combine the terms they remember from grade school with the math they have to use in physics. So, when someone says “something something hundred” you should just think “something something times 10^2.” I think I got hung up because I would try to analyze the number spoken rather than classifying it in scientific notation. That is, I had to convince my word-oriented brain terms like “thousand,” “hundred,” “billion” and so on are just older ways of denoting powers of ten.

Woo! Keep em coming!

… Please?

That’s all very nice, but I live in a country where Billion means something*10^(3+3+3+3), you still have “thousand millions” before that over here (as well as thousand billions befor trillions)… Should I consider it to be harder because of that? Should I just not care, but remember to make the conversion when speaking with an American?

@KennyR The system you refer to is maybe even easier than ours. The American system is called a Short Scale one, which means each increment (million->billion->trillion…) multiplies by 10^3. The Long Scale system (which was, up until recently, the standard everywhere else) counts by 10^6.

Consider the formula to go from prefix (mi-, bi-, tri-, etc) to number.

Short Scale: n-illon = 1000^(n+1) [i.e., one billion = 1000*1000^2]

Long Scale: n-illion = 1,000,000^n [i.e., one billion = 1,000,000^2]

With short scale, there’s that awkward extra thousand we always need to remember to start from. Yours is more concise: a quintillion just means “5 millions multiplied together”.

In my mind, the yours is MUCH cleaner, since it’s counting in log space with no weird offset. For you, 1 is the n=0 case. Ours, 1 is the n=-1 case. Indexing from -1? Shame on you, America!

I’m not sure which country you live in, but I know the UK used to use thousand millions but it got Americanised. I think most other countries will follow suite at some point.

isn’t it supposed to be a base “10″ system instead of “3″ since the exponent is any number and the base is always 10? Now i’m confused

Right. I keep forgetting that a huge chunk of the English-speaking Internet is from the USA. And hence not as intimately familiar with the metric system (and hence SI) when they get to university. As a Canuck, I’ve been dealing with metric prefixes since I was about 8, and had that all figured out long ago.

Also, since you plan on doing this for a while, I can’t wait until you get to the point where you switch away from SI units and over to a ‘natural’ unit system, where you start treating ‘c=1′, and talking about things massing so many electronvolts.

A tip from a fellow physics student: you don’t really use million/trillion/billion to describe powers of ten in physics. You use mega-, giga-, tera- etc. Check out this page: http://www.unc.edu/~rowlett/units/prefixes.html

So important but so, so, SO boring for a new student! This is yet another place where the organization of most textbooks drives me batty. (I feel like there’s a conspiracy of fibs surrounding these sections: professors pretend to expect students to read them, and students pretend that they did.) Authors! Just sneak this crucial stuff in during your first chapter on motion!