Ones Digit of 3^100
Date: 08/18/99 at 22:25:53 From: Stacy Payne Subject: Exponents of 100 What is the number in the ones place of the value of 3 to the 100th power, and what is the reasoning? I have found that the answer is 3486784401, but the reasoning has me stumped.
Date: 08/19/99 at 08:31:08 From: Doctor Rick Subject: Re: Exponents of 100 Hi, Stacy. I don't know what your answer means. The number in the ones place must be a digit, 0 to 9. If you worked out the whole answer for 3^100 (3 to the 100th power), you would get a number with 48 decimal places, so your answer isn't that, either. Ah, I found it: your number is 3 raised to the 20th power. You stopped too soon - but don't bother to keep going. My calculator can tell me what 3^100 is, but it only gives me the most significant digits, so I can't tell what digit is in the ones place. There is a trick you can use to find the ones digit. I don't want to give it all away, but you can find it if you look for a pattern. Fill in this table: n 3^n - --- 0 1 1 3 2 9 3 : 4 5 6 7 8 : Once you see the pattern, you will be able to find the ones digit for any power of 3. But I hope you'll also want to try to understand the reason for the pattern; that's really the only way to be sure the pattern goes on forever. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.