Relative error equation question (math help)

[polarmystery]

I got a question for a problem. I am trying to find the general equation for a relative error equation but I'm having some difficulty in the answer format. I'm probably overlooking something really simple. Anyway, here it is.

[FONT=&quot]What is the general formula for the relative error in using 2^10k as an approximation for 10^3k? Write your answer in the form α^k-1 for some number α.[/FONT]

The formula for relative error percent is [FONT=&quot]dx =( x0[/FONT]/x) - 1 then x 100 for percent. and so far I came up with [FONT=&quot](1/5)^7k [/FONT]but I don't understand where the k-1 term would come from? Any help? Thanks in advance.

edit for equation error.

The answer needs to be in a simplified format still keeping the k's intact.

 

[rcpratt]

I'm confused. Relative error is dx=(x0-x)/x=(x0/x)-1. I guess that's what your equation says, although your use of parenthesis and spacing confused me.

= (210k/103k)-1 = 103.9%?

I'm missing some important information about these k's, I feel like.

 

[polarmystery]

I'm not sure what I have now is correct at this point