# Can a half life be stated in terms of percentage loss?

Radioactive decay and other phenomena are measured in terms of half lives. I think this is just an easily-comparable way of stating a repeated percentage loss, but my mathematical knowledge is very weak.

As a crutch, I wrote a program to start with 1,000,000, multiply by 0.999, and repeat. I had it print a message every time it reached a halving - that is, when the remaining amount was 500,000 or less, then 250,000 or less, etc. I saw a consistent half life of 693 rounds:

reached 499900.2346477281  at round 693  - 693 rounds elapsed
reached 249900.24460085342 at round 1386 - 693 rounds elapsed
reached 124925.1909144911  at round 2079 - 693 rounds elapsed
reached 62450.132251566276 at round 2772 - 693 rounds elapsed
reached 31218.83576633967  at round 3465 - 693 rounds elapsed
reached 15606.30332502206  at round 4158 - 693 rounds elapsed
reached 7801.594694162155  at round 4851 - 693 rounds elapsed
reached 3900.019018238128  at round 5544 - 693 rounds elapsed
reached 1949.6204223478458 at round 6237 - 693 rounds elapsed
reached 974.6157066056886  at round 6930 - 693 rounds elapsed
reached 487.2106204235443  at round 7623 - 693 rounds elapsed
reached 243.55670347259502 at round 8316 - 693 rounds elapsed
reached 121.75405321597741 at round 9009 - 693 rounds elapsed
reached 60.864879771978956 at round 9702 - 693 rounds elapsed
...


Changing the decay percentage gives me a different half life, but still a consistent one.

This leads me to believe that any half life could be stated in terms of percentage decay, such as "X% of the amount decays every Y seconds/days/years". But all I have is an experiment, not a proof.

Is my idea mathematically correct?