Tuesday, November 23, 2004

The choice

When a number is expressed in scientific notation, the number of significant figures is the number of digits needed to express the number to within the uncertainty of measurement.

Say, we have eight thousand and two hundred.

Using scientific notation, this can be written as:

a) 8.2 x 10^3 - This representation has two significant digits. This means the number can be anything between 8200 and 8299.

b) 8.20 x 10^3 - This representation has three significant digits. This means the number can be anything between 8200 and 8209.

c) 8.200 x 10^3 - This representation has four significant digits. This means the number is exactly 8200.

Also in a mathematical operation, the result contains exactly the same number of significant digits as the operand with the least number of significant digits.

So, if you were to add up 2.3 and 4.62, you'd get 6.92. But really, the correct answer is 6.9.

Impossible, unlikely, improbable, possible, probable, likely, certain - Myriad summaries that we can choose from while we assess a prediction or a future, in general.

What's your significant pick?


Huckleberry Finn said...

My pick is 42, Your Honour. Haven't I told you that the answer to Life, the Universe, and Everything is 42 ?!!!


Usha said...

And to think I say " was there a choice?" so often!!

Souvik said...

Just two connections I wanted to make between mathematics & life in general.

How an entity is represented decides what it means to other to a large extent. So 8200 can have multiple interpretations depending on how it is represented. And since this is part of mathematics, our most exact science; it really has multiple possibilities in life in general, which is a lot more aribtrary.

Secondly, the choice of this representation is, or should be, determined by what leads to it i.e. the information/perception that leads us to that representation. An excact representation is limited to to the certitude of the information entity we are least certain of. This means, that this representation is only so much certain, & therefore true, but no more.

So since words represent the world we live in, we should choose carefully.

How are things otherwise?