How Do You Determine the Unit Digit of a^b?

  • Thread starter Thread starter PrudensOptimus
  • Start date Start date
  • Tags Tags
    Unit
Click For Summary
To determine the unit digit of a^b, one can analyze the unit digits of powers of a fixed base a while varying b. This approach reveals patterns in the unit digits that repeat periodically. For example, the unit digits of powers of 2 show a cycle: 2, 4, 8, 6. By identifying the cycle length and using the exponent b modulo this length, the corresponding unit digit can be determined. This method provides a systematic way to find the unit digit for any positive integers a and b.
PrudensOptimus
Messages
641
Reaction score
0
Hi, is there any way to find Unit Digit of a expression, say

a^b


where a, b, are positive integers?
 
Mathematics news on Phys.org
Yes.

Hint: fix a, vary b, and ignore the irrelevant details, see if you can find a clue...
 
U mean a pattern?

Like 2^2 = 4, like 2^2222 = 4? Because 2222 is divisible by 2?
 
I mean something a little more rigorous. :smile:

Consider the values of 2^1, 2^2, 2^3, ...
 

Thread 'Leibniz Rule Videos on Digital-University'

Good morning I have been refreshing my memory about Leibniz differentiation of integrals and found some useful videos from digital-university.org on YouTube. Although the audio quality is poor and the speaker proceeds a bit slowly, the explanations and processes are clear. However, it seems that one video in the Leibniz rule series is missing. While the videos are still present on YouTube, the referring website no longer exists but is preserved on the internet archive...
View full post »

Similar threads

High School How to pick some numbers out of 13 integers, by a 4 digits code
  • · Replies 4 ·
Replies
4
Views
2K
MHB Recreational Number Theory, Unsolved Problem
  • · Replies 1 ·
Replies
1
Views
2K
MHB Determine how many licence plates would cost $100
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Rotation of a vector along two axes (of which one is angle-dependent)
  • · Replies 7 ·
Replies
7
Views
2K
MHB Find the Two-Digit Number: Exceeds by 4 and 1 Less Than Twice the Units Digit
  • · Replies 3 ·
Replies
3
Views
3K
High School Why Do We Draw Dimensionless Unit Vectors in Diagrams?
  • · Replies 16 ·
Replies
16
Views
4K
Undergrad Proof of Differences of Odd Powers
  • · Replies 11 ·
Replies
11
Views
2K
High School Confused about ciphers in the book 'Arithmetic for the Practical Man'
  • · Replies 13 ·
Replies
13
Views
2K
High School Can modular arithmetic help us find remainders and unit digits?
  • · Replies 1 ·
Replies
1
Views
1K
High School To calculate the polar unit vectors using rotated coordinates
  • · Replies 1 ·
Replies
1
Views
2K