e approximation

I ran across the approximation e ≈ 2721/1001 recently. What makes this remarkable is its accuracy relative to the size of the denominator. You can create a trivial approximation just by truncating a decimal expansion e ≈ 2718/1000 but this is only good to four significant figures, but 2721/1001 is good to seven, almost eight, significant figures. e = 2.71828182… 2721/1001 = 2.71828171… The comparison is more impressive in binary. $ bc -l >>> obase=2 >>> 2721/1001 10.10110111111000010100… >>> e(1) 10.10110111111000010101… The denominator is a 10-bit number but the approximation is accurate to 21 bits.The post e approximation first appeared on John D. Cook.