what is the digit at unit's place of 9^n?
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Answered by
8
We have the following two cases:
If n is even, then units digit of 9^n will be 1
If n is odd, then units digit of 9^n will be 9
If n is even, then units digit of 9^n will be 1
If n is odd, then units digit of 9^n will be 9
Answered by
13
Let's consider these
9^1 = 9
9^2=81
9^3=729
9^4=6561
9^5=59049
9^6=531441
As we can see , That for powers 1 , 3 and 5 the unit digit is 9. What's the thing common between 1,3 and 5? They are all odd numbers.
So, we can say that in 9^n when n = odd number, the digit at unit place = 9
Similarly for powers 2 ,4 and 6 , which are all even , unit digit is 1.
So, in 9^n , when n = even number then digit at unit place = 1.
Answer) In 9^n unit digit is 9 when n = odd number and unit digit is 1 when n = even number.
9^1 = 9
9^2=81
9^3=729
9^4=6561
9^5=59049
9^6=531441
As we can see , That for powers 1 , 3 and 5 the unit digit is 9. What's the thing common between 1,3 and 5? They are all odd numbers.
So, we can say that in 9^n when n = odd number, the digit at unit place = 9
Similarly for powers 2 ,4 and 6 , which are all even , unit digit is 1.
So, in 9^n , when n = even number then digit at unit place = 1.
Answer) In 9^n unit digit is 9 when n = odd number and unit digit is 1 when n = even number.
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