No not very far...ONLY two or three Miles. It will carry enough energy to do serious injury or death for a long time.
It is normal for hunters up north to drop moose at 500 to 800 yards with the 303 British using 180 or 200 grain rounds.
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Maybe the bullet will stay in the bear.
i sported a 6.5x55. was a good all around choice when bushwacking northern ontario.
You do know that a 180gr .303 zeroed at 200 yds will have a -60" (5 FEET ) hold over for it to hit a target at 500 yd and will have less than 1,000 ft/lbs of energy (ethical minimum to kill a deer).
So you might not be stretching it to say hunters are killing deer with it at 800 yds HaHa...
Only wealthy southern hunters had those. I was 21 years old before I found out there was someone beside Dominion Arms that made rifle ammo. That was the year I finally ran out of the ammo I got for my Birthdays and in my Xmas stocking since I was 9 years old.
I miss my No 4 rifle.