Approximately how many half-lives must pass for the amount of radioactivity in a substance to decrease to below 1% of its initial level?

7.

Explanation:

The half-life is the time needed to a radioactive element to decay to its half initial concentration.

The first half-life: decay from 100 % → 50 %.

The second half-life: decay from 50 % → 25 %.

The third half-life: decay from 25 % → 12.5 %.

The fourth half-life: decay from 12.5 % → 6.25 %.

The fifth half-life: decay from 6.25 % → 3.125 %.

The sixth half-life: decay from 3.125 % → 1.5625 %.

The seventh half-life: decay from 1.5625 % → 0.78125 %.

So, the substance to decrease to below 1% of its initial level takes 7 half-lives