Uploaded July 2010 | Updated September 2026, 3 weeks ago
This video is a lead-in to a written essay available on the website that explains Benford's Law. Here we prove, ever so swiftly(!), that about 5.8% of the powers of two begin with a seven! (And be the end of the video you will be able to prove that just under 10% of those actually begin with 77 and just under 10% of those with 777!)
This video is a lead-in to a written essay available on the website that explains Benford's Law. Here we prove, ever so swiftly(!), that about 5.8% of the powers of two begin with a seven! (And be the end of the video you will be able to prove that just under 10% of those actually begin with 77 and just under 10% of those with 777!)



![Fractions take up No Space: Rationals Have Measure Zero (TANTON Mathematics)
How much space do the fractions take up on the number line? NONE!
In this video we add up pieces of ribbon to prove that the fractions have measure zero. It is all very easy and very perturbing because it is easy!
[This video does assume familiarity with the geometric series formula - so you might want to watch a video on that too. I do that with paper tearing!] Fractions take up No Space: Rationals Have Measure Zero (TANTON Mathematics)](https://i.ytimg.com/vi/j2QAhOCdm_o/mqdefault.jpg)






