Approximations of square roots/2

This is a list of all fractional approximations of the square root of 2 (√2). The first 50 decimal digits of √2 are 1.41421356237309504880168872420969807856967187537694.

2-5 digits

 * 17/12 = 1.417... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 2 decimal digits)
 * 41/29 = 1.4138... (convergent of √2's continued fraction; 2 decimal digits)
 * 99/70 = 1.41429... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 4 decimal digits)
 * 239/169 = 1.414201... (convergent of √2's continued fraction; 4 decimal digits)
 * 577/408 = 1.414216... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 5 decimal digits)
 * 30,547/21,600 = 1.41421296... (5 decimal digits)

6-10 digits

 * 1,393/985 = 1.4142132... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 6 decimal digits)
 * 3,363/2,378 = 1.4142136... (convergent of √2's continued fraction; 6 decimal digits)
 * 8,119/5,741 = 1.41421355... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 7 decimal digits)
 * 19,601/13,860 = 1.414213564... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 8 decimal digits)
 * 47,321/33,461 = 1.4142135621... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 9 decimal digits)
 * 114,243/80,782 = 1.4142135624... (convergent of √2's continued fraction; 9 decimal digits)
 * 119,501/84,500 = 1.41421302... (6 decimal digits)
 * 275,807/195,025 = 1.41421356236... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 10 decimal digits)

11-15 digits

 * 665,857/470,832 = 1.414213562375... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 11 decimal digits)
 * 1,607,521/1,136,689 = 1.4142135623728... (convergent of √2's continued fraction; 11 decimal digits)
 * 3,880,899/2,744,210 = 1.4142135623731... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 12 decimal digits)
 * 9,369,319/6,625,109 = 1.414213562373087... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 13 decimal digits)
 * 22,619,537/15,994,428 = 1.414213562373096... (convergent of √2's continued fraction; first approximation by denominator to be accurate to 14 decimal digits)