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What is the unit digit of 3^102?
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01 Sep 2021, 10:51
01 Sep 2021, 10:51
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Expert Reply
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Question Stats:
52% (00:41) correct
47% (00:37) wrong based on 23 sessions
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the unit digit of 3^102?
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02 Sep 2021, 07:39
02 Sep 2021, 07:39
2
Carcass wrote:
What is the unit digit of \(3^{102}\)?
A. 1
B. 3
C. 6
D. 7
E. 9
A. 1
B. 3
C. 6
D. 7
E. 9
3¹ = 3
3² = 9
3³ = 27
3⁴ = 81
3⁵ = 243
3 has a cycle of 4 (the units digit repeats every 4 powers)
This means 3^8 = ---1, 3^12 = ---1, 3^16 = ---1, etc
In other words, 3^(some multiple of 4) = 1
Since 100 is a multiple of 4, we know that 3^100 = ---1
Continuing the pattern we established earlier, we get:
3^101 = ---3
3^102 = ---9
Answer: E
Cheers,
Brent
General Discussion
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WE:Engineering (Computer Software)
Re: What is the unit digit of 3^102?
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13 Dec 2023, 08:18
13 Dec 2023, 08:18
1
We need to find the units digit of \(3^{102}\)
Lets start by finding the cyclicity of units' digit in powers of 3
\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3
That means that units digit of power of 3 has a cycle of 4
=> We need to divide the power (102) by 4 and check what is the remainder
102 divided by 4 gives 0 remainder
=> Units digit of \(3^{102}\) = Units digit of \(3^4\) = 1
So, Answer will be A
Hope it helps!
Watch this video to MASTER how to find Units digit of Power of 3
Lets start by finding the cyclicity of units' digit in powers of 3
\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3
That means that units digit of power of 3 has a cycle of 4
=> We need to divide the power (102) by 4 and check what is the remainder
102 divided by 4 gives 0 remainder
=> Units digit of \(3^{102}\) = Units digit of \(3^4\) = 1
So, Answer will be A
Hope it helps!
Watch this video to MASTER how to find Units digit of Power of 3
