"Split in" vs "split into"
Solution 1:
There's not really a "grammatical" justification for the choice, but idiomatically, we almost always use "into" with "sections"...
...whereas with "half", for example (there aren't many such examples), it's the other way around
In fact, apart from "half" I'm not sure there's any other split you can make where "into" isn't preferred. If you compare split in/into two, the preference isn't quite so marked - but that's probably influenced by the unusual usage with "half". As you go to bigger numbers, the preference for "into" is overwhelmingly reasserted.
For a (weak) justification of the idiomatic preference for split into over split in, I suggest that in numerous "compound verbs" (lapse into a coma, descend into chaos, developed into full-blown AIDS, etc.), the "into" component strongly associates with "transformation" of the primary subject.
That association very much involves the "sub-component "to", which can pass muster on its own in things like turn to stone, bring to focus, etc.. With those, you can get away with "into", but you couldn't possibly use "in".
Solution 2:
We generally use 'into' to talk about directions and destinations, while we use 'in' to talk about the positions of thing. So you have to use 'split into' in your example because the destinations of the bibliography are the sections. However we might use: (1) 'into' when we think of the division (split) itself; (2) 'in' when we think more at the end of division.
Solution 3:
I have a bibliography page which I'd like to split in/into sections
So, there is this bibliography page that you split in most cases. Whatever you split, I hope you always split into sections, because I find it to be ---sections--- the best format to do so.
I have a bibliography page which I splited into twelve sections. Yes, I presented it splitted in a recent report. Don't be afraid to split; go ahead and split comfortably! Just don't ever split into half but into halves or in half.
;) Hope that helped. I would use split into sections.
From Oxford dictionary:
Divide or cause to divide into parts or elements. ‘The river had split into a number of channels’. ‘Splitting water into oxygen and hydrogen’.
Example sentences:
‘It left me absolutely dumbfounded to see the 25-foot high walls, to see how towns have been split into two.’
‘He welcomed another measure now set to be adopted by the agency, under which the westbound carriageway will be split into two separate lanes.’
‘The development will be split into five separate blocks.’
‘Under the new scheme, the town centre will be split into 12 different zones which council bosses claim could be cleared in minutes.’
‘It takes energy to split the water molecule and release hydrogen, but that energy is later recovered during oxidation to produce water.’
‘The exam is split into 10 separate tests, which last from two minutes to 18 minutes.’
‘The water molecule is split into hydrogen ions (positively charged atoms) and oxygen.’
‘Classes, which last for 45 minutes, are split into separate sessions for babies, one- to two-year-olds, and two- to four-year-olds.’
‘This electricity splits the water molecules in an electrolyte, producing hydrogen.’
‘After much debate, it was split into two separate and distinct countries.’
‘This resulted in two items being added, no items being dropped, one item being split into two separate items, and one item having minor wording changes.’
‘The program is split into three separate phases.’
‘Her hair was pulled back into a large ponytail which was split into five separate braids.’
‘But when did the Olympics split into separate Summer and Winter Games, and where were the first Winter Olympics held?’
‘The playing field is split into three separate areas: surface, air, and underground.’
‘The cotton country on this farm is split into two separate developments of about 1250 acres each.’
‘The flow of coolant when entering our heatsink base is split into six separate channels and two separate directions.’
‘The response was split evenly - 44 percent didn't work; 44 percent did work.’
‘The retail business of both his Florida and New Mexico stores was split evenly between new and pre-owned vehicles.’
‘Sozopol is split into two main parts: the old town and new town - known as Harmanite.’