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What is the ones digit in the number 3^20997

What is the ones digit in the number 3^20997-example-1

1 Answer

4 votes

Answer:

7

Explanation:

3^0 = 1

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

3^5 = 243

3^6 = 729

3^7 = 2187

3^8 = 6581

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You can see that the pattern is beginning to repeat itself.

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So all you need do is take 2099 and divide by 3. You must pay attention to the remainder.

2099 / 4 = 524.75

The answer means that you go through the cycle 524 times getting 1,3,9,7,1 as the units digit.

In this case the remainder is 0.75 which is the same as 3/4. The remainder then is 3

If there is no remainder, the ending is a one.

if there is a remainder of 1 the answer is 3

If there is a 2 remainder, the number ends in 9

If there is a 3 remainder, the number ends in 7

And that's your answer.

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