The phrase "significant fraction" refers to a considerable or important part of a whole. It indicates that the portion being referred to is notable or meaningful in size or importance. Full definition
Because the nucleus of these heavy atoms is highly charged, the electrons start to move at significant fractions of the speed of light. (sciencedaily.com)
This may not sound like a very significant fraction of the parasite population, but the average person with malaria might have a billion parasites inside them. (yourgenome.org)
Significant fractions went into health care (almost half of biomedical Ph.D. s), manufacturing (about a quarter of physical science and engineering Ph.D. s), and education (about half of social science Ph.D. s). (sciencemag.org)