Question

How to find unit digit in number system

Answer 1

Here is your answer.

If you want to find unit digit of any number Right most number is unit digit.

For example

In 999 ,9 is a unit digit

Hope it helps you

Answer 2

The digits 0, 1, 5 and 6 have a similarity in the unit digit such that

$0^n$ = 0  

$1^n$ = 1  

$5^n$ = 5 is the unit digit of the value

$6^n$ = 6 is the unit digit of the value

So, 0, 1, 5 and 6 have 0, 1, 5 and 6 as their unit digits respectively.

The digits 4 and 9 have two-unit digits alternatively

$4^1$= 4  

$4^2$ = 16  

$4^3$ = 64  

So, the unit digit varies between 4 and 6 for even and odd powers

$4^n$ = 6 is the unit digit if n is even

$4^n$ = 4 is the unit digit if n is odd

$9^1$ = 9  

$9^2$ = 81  

$9^3$ = 729  

So, the unit digit for nine varies between 9 and 1

$9^n$= 1 is the unit digit if n is even

$9^n$ = 9 is the unit digit if n is odd

For 2, 4, 7 and 8 the cyclicity of unit digit varies between 4 digits

$2^1 = 2\\ \\2^2 = 4 \\\\2^3 = 8 \\\\2^4 = 16\\ \\2^5 = 32$

 

So, the unit digits for 2 are 2, 4, 8 and 6

Similarly, the unit digits for 3 are 3, 9, 7 and 1

The unit digits for 7 are 7, 9, 3 and 1

The unit digits for 8 are 8, 4, 2 and 6

Number                Cyclicity               Unit digit

   1                                1                           1

  2                              4                          2, 4, 8, 6

  3                               4                          3, 9, 7, 1

  4                               2                          4, 6

  5                              1                           5

  6                              1                           6

  7                              4                          7, 9, 3, 1

  8                              4                          8, 4, 2, 6

  9                              2                          9, 1

 10                              1                           0

Unit digit of $4^{345}$

435 is odd so the unit digit of above number is 6

Unit digit of $7^{234}$

The cyclicity of 7 is 4

So, divide 234 by 4. We get a reminder 2

9 is the unit digit for the above number.