Question

what is the unit digit in 27^20

Answer 1

Unit digit of 27^1 =7 ( 7^1 =7)

,, ,, ,,, 27^2 =9 (7^2 =49)

UD of 27^3 =3 (7^3 =343)

UD of 27^4=1 (7^4=2401)

Hence for every four consecutive powers, the unit digit will follow a pattern of 7,9,3,1.

Hence UD of 27^20 will be 1.

Answer 2

Given:

A number in the exponential form 27^20.

To Find:

The units digit of the expansion of the above number is?

Solution:

1. The given number is 27^20. It can be also written as,

=> 27^20 = ( 20 + 7 )^20,

2. The units digit of powers of any number ending with 0 is always 0 in all the cases. ( Except 0 power 0 which is not defined ).

3. The units digit of 7^20 can be calculated as follows,

=> The units digit of$7^n$ is,

• 7 for 4n + 1 type values
• 9 for 4n + 2 type values
• 3 for 4n + 3 type values
• 1 for 4n type values

=> 20 can be written as 4(5) which is a 4n type value.

=> Hence the units digit of 7^20 is 1.

Therefore, the units digit of 7^20 is 1.