A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

Accurate at 99.9999746%

Explanation:

First of all, let's calculate how many seconds we have in a year which has 365 days.

1day = 24 × 60 × 60 seconds = 86400 s

Thus, for 365 days, we have;

86400 × 365 = 31536000 seconds

Now, since 1 year has 31536000 seconds, let's find the ratio of efficiency.

We are told that the watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. Thus, efficiency is given by;

Efficiency = (8/31536000) × 100% = 0.00002536783 %

Thus, it will be be accurate at;

100% - 0.00002536783% ≈ 99.9999746%