If a quasar has a redshift of 3.3, at what fraction of the speed of light is it moving away from us?

The quasar is moving with 0.68 the speed of light.

Explanation:

let v be the speed quasar is moving with away from us, z be the redshift and c be the speed of light.

Using the relativistic doppler shift formula, the fraction of the speed of light that the quasar is moving away from us is given by:

v/c = [ (z - 1) ^2 - 1]/[ (z - 1) ^2 + 1]

= [ (3.3 - 1) ^2 - 1]/[ (3.3 - 1) ^2 + 1]

= 0.68

Therefore, the quasar is moving with 0.68 the speed of light.