Explanation Given: Let p = p 1 .... p s be an integer with digits p 1 ..... p s . Calculation: Let p = p 1 .... p s be an integer with digits p 1 ..... p s . Let y = 0. p 1 ...... p s ¯ . … (1) It means y = 0. p 1 p 2 ... p s p 1 p 2 ... p s and so on . Also, we can rewrite it as: y = 0. p 1 p 2 ... p s p 1 p 2 ... p s ¯ Multiply both sides by 10 s . 10 s y = p 1 p 2 ... p s p 1 p 2 ... p s ¯ … (2) Subtract equation (1) from equation (2). 10 s y − y = p 1 p 2 ... p s p 1 p 2 ... p s ¯ − 0. p 1 p 2 ... p s ¯ Solve the above equation. ( 10 s − 1 ) y = p 1 p 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 1.1, Problem 84E

To determine

Show that p10s−1=0.p1....ps¯.

Use this to find the decimal expansion of r=211.

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Chapter 1.1, Problem 83E

Chapter 1.1, Problem 85E

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Chapter 1 Solutions

Calculus - Standalone book

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 p 10 s − 1 = 0. p 1 .... p s ¯ . Use this to find the decimal expansion of r = 2 11 .

Solution Summary: The author explains how to determine the decimal expansion of r=211.

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Show that p10s−1=0.p1....ps¯.

Use this to find the decimal expansion of r=211.

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Chapter 1 Solutions

Show that p 10 s − 1 = 0. p 1 .... p s ¯ . Use this to find the decimal expansion of r = 2 11 .

Solution Summary: The author explains how to determine the decimal expansion of r=211.

Concept explainers

Videos

Show that p10s−1=0.p1....ps¯. Use this to find the decimal expansion of r=211.

Want to see the full answer?

Chapter 1 Solutions

Show that p10s−1=0.p1....ps¯.

Use this to find the decimal expansion of r=211.