The decimal representation of a positive integer a is given by a = an-1an-2a₁a0 where a = an-110n-¹ + An−210¹−² + + a₁10 + ao and the digits an-1ªn-2a₁ª₁ are in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with an-1 ‡ 0. In this case we say that the integer a is an n 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-2a₁a0 where a = an-110n-¹ + An−210¹−² + + a₁10 + ao and the digits an-1ªn-2a₁ª₁ are in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with an-1 ‡ 0. In this case we say that the integer a is an n 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
Section1.2: Exponents And Radicals
Problem 91E
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![The decimal representation of a positive integer a is given by a = an-1 ªn-2 ··· A₁ ao where
a = an-110¹-¹+ an-210¹-² + + a₁10 + ao
and the digits an-1an-2 ··· A₁ ao are in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with an-1 # 0. In
this case we say that the integer a is an n digit number or that a 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 10¹-1< a < 10". Use this inequality to prove that n [log₁0 a] + 1.
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Transcribed Image Text:The decimal representation of a positive integer a is given by a = an-1 ªn-2 ··· A₁ ao where
a = an-110¹-¹+ an-210¹-² + + a₁10 + ao
and the digits an-1an-2 ··· A₁ ao are in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} with an-1 # 0. In
this case we say that the integer a is an n digit number or that a 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 10¹-1< a < 10". Use this inequality to prove that n [log₁0 a] + 1.
=
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