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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#4. Thanks.
![4. The decimal representation of a positive integer a is given by a = an-1ªn-2a₁ª0 where
a = an-110n-1 + an-2-
210¹-² +
+ a₁10 + ao
and 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. 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 10¹-1< a < 10". Use this inequality to prove that n= [log₁0 a] + 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2F539cf100-fc14-437d-b374-e4bc0c0abe06%2Fbas1km4_processed.png&w=3840&q=75)
Transcribed Image Text:4. The decimal representation of a positive integer a is given by a = an-1ªn-2a₁ª0 where
a = an-110n-1 + an-2-
210¹-² +
+ a₁10 + ao
and 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. 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 10¹-1< a < 10". Use this inequality to prove that n= [log₁0 a] + 1.
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