Question

what is the digit at unit place of 9n

Answer 1

Answer: If n is even, unit digit is 1. If n is odd, unit is 9.

Step-by-step explanation:

Since 9n has different unit digits for different values, i believe your question seeks 9^n.

Let's start with n = 1,

Then ⇒9^n = 9^1 = 9

For n = 2,

Then ⇒9^n = 9^2 = 81

For n = 3

Then ⇒9^n = 9^3= 729

For n = 4,

Then ⇒9^n = 9^4= 6561

So we see regular change in the unit digit and this continues.

Let's see in other way,

9^n

= (3^2)^n

= 3 ^2n

So, Since 3^2n will have to end with 9 or 1 ( We know that, 3 * 3 = 9, 3 * 3 * 3 *3 = 1)

Therefore, 9^n ends in either 9 or 1.