Question: Suppose that f l(y) is a k-digit rounding approximation to y. Show that |y fl(y)/y| 0.5 10k+1. [If dk+1 < 5, then

Suppose that f l(y) is a k-digit rounding approximation to y. Show that |y − fl(y)/y| ≤ 0.5 × 10−k+1. [If dk+1 < 5, then f l(y) = 0.d1d2 . . . dk ×10n. If dk+1 ≥ 5, then f l(y) = 0.d1d2 . . . dk ×10n + 10n−k .]

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