By no means a direct or definitive answer, just three references: the 1st on estimating in college-level engineering, the 2nd more speculative at the research level in mathematics and theory of computation, the 3rd just for fun (at middle-school level).
(1) Rebecca Bourn, Sarah Baxter. "Developing Mathematical Intuition by Building Estimation Skills." 2013 ASEE Annual Conference & Exposition. Download link
By thinking critically about the validity and purpose of particular numbers and applying them outside the bounds of their standard usage, students show mastery of comprehension and move on to the pedagogical realms of application and creation.
(2) Richard Lipton (blog). Mathematical Intuition—What Is It?. Oct. 2010.
Open Problems. Is intuition simply built up by learning more and more about an area? Or is intuition something that is separate from just being an expert in an area? Can you be quite strong in an area and still have weak intuition, or is that impossible?
(3) Robert Kaplinsky, 2013: How Much Money IS That?!.
[![Cash][1]][1]
Assume all \\\$100US\\\$100 bills.
>! About $220,000,000, i.e., nearly a quarter-billion US dollars.