It's common terminology - a one in two chance in a coin toss does not mean you will get one head in two flips.
If you understood statistics, you would realise it is impossible to express figures in the way you desire - I'm not having a go or expecting that you should, as it's university level stuff, but there is a reason things aren't as simple as you would naively expect.
One in 100 years is an expectation value
- the average number of events expected over a 100 year period will be one. The expectation value is simple for discrete events like flipping a coin, for example, the expectation value for heads of 100 flips is 50. However, to deduce such things for continuous events you need to use calculus, and it gets messy.
In this case the probability for a one in T year event occurring once (or importantly, more) over n years is:
P = 1 - (1-1/T)^n
Ie. over 100 years the probability it occurs once or more is 63.40%, and thus for it not occurring 36.6%. Over one year the probability of at least one event is 1%, with a 99% chance it doesn't occur. The messiness comes from the need to consider infinitesimal time (ie. the probability of the event occurring over a infinitely small time frame) which allows for the possibility of more than one event in a given year. There is also a static assumption, which explains why 1:100 year events tend to be clustered.
Consider simply a 1:5 yr event, ignoring for simplicity the possibility of more than one event a year (ie. simply stating that the event either does or does not occur in a given year):
The probability of it occurring in a year is 1/5, and not 4/5, then the probability of N events in five years is:
Pr(N) = A(N) x (4/5)^(5-N) x (1/5)^N where N is the number of possibilities of the order of the event occuring, ie.
For 5 years, there are 2^5=32 possibilities of how the events are ordered
The expected number of events is the probability of that number of events by that number of events:
Ie. Expected value = ~0.33*0+0.41*1+0.20*2+0.051*3+0.0064*4+0.00032*5 = 1
Note that 2 events has a probability of 20%, and three of 5%, so not completely unexpected. For completion we really need to consider multiple events in a year which will change the probabilities slightly (since we have possibilities of N=6,7,8...) but isn't really necessary for low probability events, and won't change the expected value.
However, using proper English, "one in a hundred years" cannot possibly mean, "a one percent chance in any given year." The two expressions are mutually contradictory.
As you can see, a probability of 1% in a year gives an expected 1 event in 100 years - they mean the same thing.