Unit digit of number system

 

                                              3.Unit digit of number system (only 3 Rule)

Rule (1): - same number and same unit digit

Digits 0, 1, 5, and 6:

 

Example: -

0⁵ = 0: unit digit is 0, the number itself.

1⁷ = 1: unit digit is 1, the number itself.

5³ = 5: unit digit is 5, the number itself.

6⁴ = 6: unit digit is 6, the number itself.

 

Question 1: Find the unit digit of 756³⁴⁵.

 

Answer: Simply find 6³⁴⁵ which will give 6 as a unit digit, hence the unit digit of 756³⁴⁵ is 6.

 

Question 2: Find the unit digit of 345³²⁴⁵⁶.

 

Answer: Find 5³²⁴⁵⁶ which will give 5 as a unit digit, hence the unit digit of 345³⁴⁵⁶⁶ is 5.

 

 

Rule (2): - Power of odd then unit same and power of even then case of ‘4’ 6 unit and case of ‘9’ 1

Digits 4, 9

 

Example: -

4² = 6: if 4 is raised to the power of an even number, unit digit will be 6.

4³ = 4: if 4 is raised to the power of an odd number, unit digit will be 4.

9² = 1: if 9 is raised to the power of an even number, unit digit will be 1.

9³ = 9: if 9 is raised to the power of an odd number, unit digit will be 9.

Question 1: Find the unit digit of 414²³.

 

Answer: 23 is an odd number, so 4^odd=4, hence the unit digit is 4.

 

Question 2: Find the unit digit of 29⁸².

 

Answer: 82 is an even number, so 9^even=1, hence the unit digit is 1.

 

Rule (3): Division rule of 4 then factoring the remainder to find unit digit

Digits 2, 3 and 7, 8 (Repeat 4-digit form)

 

1. 2¹ = 2, unit digit is 2.

2. 2² = 4, unit digit is 4.

3. 2³ = 8, unit digit is 8.

4. 2⁴ = 16, unit digit is 6.

5. 2⁵ = 32, unit digit is 2.

 

Question 1: Find the unit digit of 257³⁴⁵.

 

Answer: 345/4 = 1, so 7¹, hence the unit digit is 7.

 

Question 2: Find the unit digit of 423⁴³.

 

Answer: 43/4 = 3, so 3³, hence 7 is the unit digit.

 

Question 3: Find the unit digit of 28¹⁴⁶.

 

Answer: 146/4 = 2, so 8², hence the unit digit is 4.

 

Question 3: Find the unit digit of 342⁸¹².

 

Answer: 812/4 = 0, so 2⁴, hence the unit digit is 6.

 

Note: प्रश्न 3 के अनुसार, यदि 812 को 4 से भाग दिया जाए, तो परिणाम 0 प्राप्त होता है। ऐसी स्थिति में, 2 की घात 4 का इकाई अंक ही हल होगा। यह नियम 2,3,7,8 पर भी लागू होगा।