Rocket equation: what fraction remains after reaching 1100 m/s exhaust speed?

[gadabout1018]

Homework Statement

Obviously, we can make rockets to go very fast, but what is a reasonable top speed? Assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible.


If the rocket ejects gas at a relative speed of 1100 and you want the rocket's speed eventually to be 1.00×10−3 c, where c is the speed of light, what fraction of the initial mass of the rocket and fuel is not fuel

Homework Equations

v=v(ex)ln(m/m0)
v1=1100lm(m/m0)

The Attempt at a Solution

i think I am having trouble finding the final velocity. I did another poblem were the final velocity was 4000 m/s and i got it correct.

 

[JasonGodbout]

The final velocity is 1.00×10−3 c.

 

[gadabout1018]

that is what i thought but when i try in on mastering physics i get in incorrect

 

[JasonGodbout]

Try e¹⁰⁰ then e²⁰⁰ and you will see why.