what would your power usage in wh/mile be?
if you don't know that, then:
what is your weight (bike and you and anything you would carry), terrain, wind, speed, riding style (lots of stops/starts, hard acclerations, or long continous rides at one speed, etc), and how much assistance do you need from it, and are you going to be shifting gears appropriately as needed, or always riding in one gear, etc etc. ?
knowing those will help you figure out how much power you need, which will help you know how much you'll use each mile, which will help you know how much you'll need for a hundred of them.
as an example, typical riding around at 20mph will probably take an average rider on flat terrain around 10wh/mile.
the same but at 10mph would probably take less than 5wh/mile, because there's a lot less air resistance at lower speeds.
the same but at 25mph, for the same reason, would probably take up to 20wh/mile.
if there's a lot of stops and starts, or hills, you might double the wh/mile figure.
let's go back to that first scenario, 10wh/mile. if that's all you use, then 10 x 100 miles = 1000wh for a battery, which for a 48v battery is around 21ah, minimum. that's kind of a big battery, but not huge. would probably weigh less than 17-20lbs, depending on chemistry and casing, and probably be around the size-ish of a 50cal ammocan (shape could vary a lot depending on cell type used).
always better to use a bigger battery than you need, because:
--as it ages, it'll have less capability and capacity. some cell types age faster than others, and depending on their usage it can be even worse.
--if you end up with headwinds or detours, you'll need more capacity to give you the same range.
i usually go with 20-30% extra, at least, for just-in-case. more, if your conditions and routes are more variable, maybe up to another 50%.
so you might need 1300-1500wh if you needed a lot extra just-in-case capacity. 1500wh would be around 32ah. this is a pretty big and heavy battery, getting to the 25-30lb range.
if your riding used 20wh/mile, you'd need a battery twice as big as the above estimates.
if your riding uses a lot more, then a much bigger battery.
if a lot less, then a much smaller one.