Find Unit digit

Unit digit

The unit digit of any number is called that which is on the one's place of the number, in other words, the first place from the right e.g.- the unit digit of 28 is 8, the unit digit of 279 is 9, the unit digit of 24560 is 0 and so on.

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There are total 10 digit in maths 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 divide them into three parts (2, 3, 7, 8), (5, 6, 0, 1 ) and (4, 9)

How to find the unit digit of 2, 3, 7, 8?

If the unit's place of a number is 2, 3, 7, 8 and it is in power, then to get the unit digit, divide the power by 4, the remainder is written in the power if the remainder is 0, so put 4 in the power. Let us understand this with some questions.

e.g.- 

Qus. What is the unit digit of 2⁴³ ?

Solution-

= 2⁴³ 

= 2^43/4        [43/4 Remainder = 3]

= 2³ 

= 8 

So, the number of unit digit is 8.

Qus. What is the unit digit of 7⁴⁹ ? 

Solution- 

= 7^49/4

= 7¹       [49/4 Remainder = 1]

= 7

So, the number of unit digit is 7.

Qus. What is the unit digit of 8⁴⁰⁰ ? 

Solution- 

= 8^400/4

= 8⁰       [400/4 Remainder = 0]

= 8⁴         [The remainder is 0, so put 4 in the power.]

= 4096

So, the number of unit digit is 6. 

Qus. What is the unit digit of 333⁸⁸⁸ + 888²²² ? 

Solution- 

= 333⁸⁸⁸ + 888²²² 

= 3^888/4 + 8^222/4   [Solve by taking unit digit only]

= 3⁰ + 8²       [888/4 Remainder = 0, 222/4 Remainder = 2]

=  3⁴ + 64      [The remainder is 0, so put 4 in the power.]

= 81 +64

= 145

So, the number of unit digit is 5. 

How to find the unit digit of 5, 6, 0, 1?

Whatever is the power of all these numbers(5, 6, 0, 1), their unit digit is the same number.

e.g.- 

Qus. What is the unit digit of 5³ ?

Solution-

= 5³  

= 125

So, the number of unit digit is 5.

Qus. What is the unit digit of 5⁹ ? 

Solution- 

= 5⁹

= 1953125

So, the number of unit digit is 5.

Qus. What is the unit digit of 0⁴⁰⁰ ? 

Solution- 

= 0⁴⁰⁰      

= 0

So, the number of unit digit is 0.

Qus. What is the unit digit of 6⁸ ? 

Solution- 

= 6⁸     

=1679616

So, the number of unit digit is 6.

It is clear from all the above questions that no matter what is the power of 5, 6, 0, 1, the unit digit will get the same number. 

How to find the unit digit of 4, 9?

If the unit's place of a number is 4, 9 and it is in the power, then to get the unit's digit, first, it has to be noticed whether the power is even or odd. If the power of 4 is odd, then the unit digit will be 4 but If the power is even, the unit digit will be 6. Similarly, if the power of 9 is odd then the unit digit will be 9 but if the power is even then the unit digit will be 1.

e.g.- 

Qus. What is the unit digit of 4⁷ ?

Solution-

= 4⁷           [Odd Power]

= 16384

So, the number of unit digit is 4.

Qus. What is the unit digit of  4¹² ? 

Solution- 

= 4¹²         [Even Power]

= 1953125

So, the number of unit digit is 5.

Qus. What is the unit digit of  9⁹ ? 

Solution- 

= 9⁹                [Odd Power]

=387420489

So, the number of unit digit is 9.

Qus. What is the unit digit of  9⁸ ? 

Solution- 

= 9⁸           [Even Power]

= 43046721

So, the number of unit digit is 1.