Question

what is the last digit of 5 power 100​

Answer 1

Answer:

it will always have 5 at its unit digit untill the power is negative or zero....

Step-by-step explanation:

hope it helps...

Answer 2

Concept:

To answer this question we need the basic concept of multiplication and modulo operation.

Modulo operation gives the remainder(signed or unsigned) of a division.

Formula required:

Modulo operation with 10=10x+remainder.This means when numbers are divided by 10 what remainders we get.

To find:

We are to find the last digit of 5¹⁰⁰

Solution:

We can see the pattern by working with modulo 10.

5¹=5, this number ends with 5.

5 can be written as 10x+5 where x=0 and reminder=5, but our concentration will be on the remainders.

5²=25, this also ends with 5

25 can be written as 10x+5 where x=2 and remainder=5 again

Similarly, taking 5³=125 which again ends with 5

and 125 can be written as 10x+5 where x=12 and remainder=5.

Hence, we get a pattern :

Any number that is 5 more than a multiple of 10 (also when that multiple is 0) will be another number that is 5 more than a multiple of 10 when multiplied by 5.

This shows every power of 5 will give numbers which are 5 more than a multiple of 10; these numbers end with the last digit 5.

Thus, we get the result:  the last digit of 5¹⁰⁰ is 5