Explanation Given: The fraction is r = a b . Calculation: The fraction is r = a b . Let r be a finite decimal expansion. Such that r = 0.000..... p . We can rewrite it as: r = 0.000..... p × 10 10 s Solve the equation. r = p 10 s 10 s r = p We know that r = a b . Substitute a b in place of r

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.1, Problem 89E

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Show that a fraction r=ab in lowest term has a finite decimal expansion if and only if b=2n5m for some n,m≥0.

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Chapter 1.1, Problem 88E

Chapter 1.1, Problem 90E

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Chapter 1 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Show that a fraction r = a b in lowest term has a finite decimal expansion if and only if b = 2 n 5 m for some n , m ≥ 0 .

Solution Summary: The author explains that r=ab in lowest term has a finite decimal expansion.

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Show that a fraction r=ab in lowest term has a finite decimal expansion if and only if b=2n5m for some n,m≥0.

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Chapter 1 Solutions