Question

what is the unit digit in 5^100​

Answer 1

Step-by-step explanation

Answer 2

The correct answer is 5 is the unit digit.

Concept used:

The fundamentals of multiplication and modulo operations are necessary in order to respond to this question.

The remainder (signed or unsigned) of a division is obtained via the modulo operation.

Formula required:

Using the modulo technique, 10=10x+remainder this tells us what remainders we obtain when we divide numbers by 10.

To find:

Now we are to find the unit digit of 5¹⁰⁰

Solution:

Working with the modulo 10 number, 5¹=5, we may observe the pattern.

Although 5 can be expressed as 10x+5 with x=0 and remainder=5, we'll focus on the remainders.

This also finishes in 5 since 5²=25.

Write 25 as 10x+5, where x=2 and remainder=5 once again.

Similar to the previous example, 5³=125, which also has a remaining of 5, can be represented 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 will result in another number that is 5 more than a multiple of 10 when multiplied by 5 (this holds true even when the multiple is 0).

This demonstrates that every power of five will produce numbers that are five times larger than a multiple of ten, and these numbers always finish in five.

Thus, we obtain the outcome: 5¹⁰⁰ last digit is 5.

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