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.
Hi,
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?
Penny