Big numbers and really little ones.

Hi everyone, welcome back to Ballarat Science in the Community.

We’ve been working away over the break to organise our content for this year. I’m also really excited to say that we have several new contributors to the BSitC project, who’ll be collaborating on content throughout the year (I’ll introduce everyone as we go).

We have a lot planned for 2017. Our plan this year is to mix things up with regular topics like this one, as well as some more in depth blog posts. After looking at the list of things we want to discuss through this blog there is a bit of groundwork to lay before we get into some of the more complex topics. To start things off we thought it would probably be helpful to give those of you who have not thought about mathematics for a while, a bit of a refresher on how to deal with numbers.

In this series, we’re going to look at things like scientific notation, parts per million, scales, curves and fractals etc. Don’t worry it is not Math class and will not be all at once.

So, scientific notation.

What is it? And why is it helpful?

The idea is as follows: when we use really big numbers or really small ones, we might drop an important ‘zero’, it can confuse our readers, and it takes up valuable time and space. Instead it is just a lot easier to use what we call scientific notation.

It works like this: Take a number and multiply it by 10 to the power of x. An order of magnitude goes up by adding a zero to the number, so 1 turns into 10, turns into 100, turns into 1,000 (it’s okay, I know that reading this you might zone out, but the goal here is just to explain the basics not get bogged down by algebra).

You can see on the table below what this looks like and how it works. You have your number (in the table we’re looking at the number 1.0) and you multiply it by the base number (in this case it’s 10) “to the power” of your exponent (that’s the number to the right and above the 10.) Every time you do this you move the decimal point 1 place to the right, making the number written out bigger. Every time you make the exponent less by 1 (that’s when you can get into negative numbers) you move the decimal place to the left by 1, making it smaller. The number of the exponent equals the number of zeroes before or after the base number.

 

Table 1. Scale of scientific notation, adapted from memrise.comscientific-notation

It’s much easier to write 1.0 x 10^24  than it is to write 1, 000, 000, 000, 000, 000, 000, 000, 000 (that’s 1 with 24 zeros after it, a massive number). It also allows you to say things like 1 millimetre rather than 0.0001 metres (see the scale in this vid). That’s why we use it, it makes numbers easier to look at, understand, and manipulate.

Another common term is engineering notation that is when the exponent is changed by a factor of 3. So it goes,

1.0 x 10^9 = 1,000,000,000

1.0 x 10^6 = 1,000,000

1.0 x 10^3 = 1,000

1.0 x 10^0 = 1.0

1.0 x 10^-3 = 0.001

1.0 x 10^-6 = 0.000001

1.0 x 10^-9 = 0.000000001

You may have also heard the term “order of magnitude” before and that’s what we’re talking about here an order of magnitude tells the reader how many times you multiply your the base number by 10 or 1/10th making it either larger or smaller. Engineering notation uses much more common prefixes  like milli, kilo, mega etc as a shorthand way to indicate “order of magnitude.”

That’s enough for now. You’ll see scientific and engineering notation regularly as you read through our blogs terms like nano, pico and parsec will begin to make sense as we talk about scales, fractals and other useful mathematical tools but if you need a refresher you can always come back and read these regular “core” blogs.

I understand that all this math might be enough for some people, so here’s a vid of doodling in math from Khan Academy. (I love Khan academy, it’s been so helpful for boosting my maths skill set.)

Ask your questions, support your opinion with evidence, discuss, edify.

 Enjoy.

 

Bibliography

Khan Academy is an amazing online education resource that has hundreds (maybe thousands?) of instructional videos on everything from early maths to the theory of relativity, arts, history and politics. This is their doodling in math vid, lots of fun can and should be had with mathematics.

https://www.khanacademy.org/math/math-for-fun-and-glory/vi-hart/doodling-in-math/v/doodling-in-math-class-squiggle-inception

Memrise is another great free and fun learning tool.

http://www.memrise.com/course/150181/scientific-notation-prefixes/

See the scale of the universe from the subatomic to the breadth of the universe in this video representation.

https://www.youtube.com/watch?v=Usj6viU0AaI

 

Banner image adapted from Dr Odd

http://www.drodd.com/html7/numbers.html

 

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