In TNG episode "Suspicions" Jobril states that he is one million km from the corona of the star and will arrive in 3 minutes at 3/4 impulse.

Here is what I've worked out:

Shuttle can travel 1,000,000 km in three minute at 3/4 impulse.

(This takes no hypothetical acceleration curves in to account and assumes a constant speed.)

This means that the shuttle can travel 20 million km in one hour

20,000,000 km = 12,427,423.845 miles

1/4 impluse = 4,142,474.615 mph

Full impulse = 16,569,898.46 mph

Speed of light is 670,616,628 mph

Full impulse = 0.0247084515476702 of the speed of light