#4. Thanks. 4. The decimal representation of a positive integer a is given by a = an-1ªn-2a₁ª0 wherea = an-110n-1 + an-2-210¹-² ++ a₁10 + aoand the digits an-1ªn-2 ··· α₁ ªo are in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with an-1 ‡ 0. Inthis case we say that the integer a is an n digit number or that a is n digits long. Forexample, the number 756 = 7.10² +5∙10 + 6 and is 3 digits long.Let a E N. If a is an n digit number, then from the decimal representation given above weknow 10¹-1< a < 10". Use this inequality to prove that n= [log₁0 a] + 1.

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The decimal representation of a positive integer a is given by a = an-1ªn-2 *** α₁α where a = An-110¹-¹ + An-210¹−² + + a₁10 + ao and the digits an-1ªn-2 ··· α₁ªº are in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with añ−1 ‡ 0. In this case we say that the integer a is an ŉ digit number or that a is n digits long. For example, the number 756 = 7 · 10² +5∙10 + 6 and is 3 digits long. Let a E N. If a is an n digit number, then from the decimal representation given above we know 10n-1 < a < 10". Use this inequality to prove that n= [log₁0 a] + 1.

The decimal representation of a positive integer a is given by a = an-1ªn-2 *** α₁α where a = An-110¹-¹ + An-210¹−² + + a₁10 + ao and the digits an-1ªn-2 ··· α₁ªº are in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with añ−1 ‡ 0. In this case we say that the integer a is an ŉ digit number or that a is n digits long. For example, the number 756 = 7 · 10² +5∙10 + 6 and is 3 digits long. Let a E N. If a is an n digit number, then from the decimal representation given above we know 10n-1 < a < 10". Use this inequality to prove that n= [log₁0 a] + 1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 40E

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