Question

the unit's digit of 13^2003 is??
1) 1.
2) 3
3) 7
4) 9
please explain me the method of solving this!!

Answer 1

Answer:

7

Step-by-step explanation:

Method: Look for repeating pattern

13¹ = 13 ⇒ The value in the units place is 3

13² = 169 ⇒ The value in the units place is 9

13³ = 2197 ⇒ The value in the units place is 7

13⁴ = 28561 ⇒ The value in the units place is 1

13⁵ = 371293 ⇒ The value in the units place is 3  (repeated)

13⁵ = 4826809 ⇒ The value in the units place is 9  (repeated)

The units repeats itself every power of 4

Find the number of groups of 4:

2003 ÷ 4 = 500 Remainder 3

Therefore power of 3 will give us the value of 7 in the units place

Answer: (3) 7

Answer 2

Answer: 7

Step-by-step explanation:

13> 10+3.

You don't need to check for 13 now, instead use for 3.

1st iteration >3

2nd iteration> 3 x 3=9

3rd iteration  > 3 x 3 x 3= 27  unit digit 7

4th iteration > 3 x 3 x 3 x 3= 81 unit digit 1

5th iteration > 81 x 3 =243 (This iteration was not necessary, just for check used..)

So, we see a cycle is of 4 iterations .

So divide 2003 by 4 . Rather solving it , see 2000 is directly divisible +3 remainder.

So , your required unit digit will be unit digit of 3rd iteration i.e. 7