# Thread: Error in a qoutient

1. ## Error in a qoutient

Hi there, I'm doing some basic data handling, at the moment I'm on sources of error i.e measured values and fractional errors.

I've attached a scan of the page.

My question is how do you come to a/b(fa-fb)?
I know Q=a/b
Qm=a(1+fa)/b(1+fb)

so Qm-Q=a(1+fa)/b(1+fb) - a/b so i factorise to get a/b(1+fa/1+fb - 1)

which equals a/b(fa-fb/1+fb)...so from here I don't know how to get the result in the book.

Thanks.

2. ## Re: Error in a qoutient

Originally Posted by flashylightsmeow
Hi there, I'm doing some basic data handling, at the moment I'm on sources of error i.e measured values and fractional errors.

I've attached a scan of the page.

My question is how do you come to a/b(fa-fb)?
I know Q=a/b
Qm=a(1+fa)/b(1+fb)

so Qm-Q=a(1+fa)/b(1+fb) - a/b so i factorise to get a/b(1+fa/1+fb - 1)

which equals a/b(fa-fb/1+fb)...so from here I don't know how to get the result in the book.

Thanks.
You use a power series expansion of $\displaystyle 1/(1+f_b)=1-f_b+O(f_b^2)$ for small $\displaystyle f_b$

CB

3. ## Re: Error in a qoutient

Hi there CB,

Thanks for your reply, I've actually never touched on power series, would you be able to recommend preceding topics that I will need to study to fully understand them.

Many thanks

flm

4. ## Re: Error in a qoutient

Originally Posted by flashylightsmeow
Hi there CB,

Thanks for your reply, I've actually never touched on power series, would you be able to recommend preceding topics that I will need to study to fully understand them.

Many thanks

flm
In this case you need Newton's generalised binomial theorem.

CB