Quandaries and Queries


I am a graduate student in CT completing my masters in education.  I am currently enrolled in a math reasoning class and a math question I have to answer is determine the units digit in 3 28power.  When I set up a table and keep cubing the numbers, I find a pattern with the last digits of the numbers that follow 1,3,9,7.  My calculator gets to about the 19th power, and then I get an error.  If I continued the pattern, would the units digit then be the last digit of 3 28th power, which would be a 7?  Please let me know if I am solving this correctly and what a unit's digit actually is.

Thank you.




You have the right idea but your calculations are off slightly. The powers of 3 are

n 3n last digit
1 3 3
2 9 9
3 27 7
4 81 1
5 243 3
6 729 9
7 2187 7

So the pattern in the last digit is 3,9,7,1,3,9,7,1,... The cycle in the pattern is of length 4 and 28/4=7 so if you continue the table above to the 28th row the pattern will repeat exactly 7 times and the last digit in the 28th row will be 1.

So, what's the last digit of 32005?



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