Continued fractions
General · Mathematics
Study notes
Q: Write 415/93 as a continued fraction and find a convergent. Euclid: 415 = 93×4+43; 93 = 43×2+7; 43 = 7×6+1; 7 = 1×7+0. Quotients: 4, 2, 6, 7. CF: [4; 2, 6, 7]. Convergent [4; 2] = 4+1/2 = 9/2 = 4.5 (415/93 ≈ 4.462 - close!). [4; 2, 6] = 4+1/(2+1/6) = 4+6/13 = 58/13 ≈ 4.4615 - closer!