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Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) Notes | Study UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making - UPSC

Document Description: Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) for UPSC 2022 is part of UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making preparation. The notes and questions for Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) have been prepared according to the UPSC exam syllabus. Information about Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) covers topics like and Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) Example, for UPSC 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds).

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Shortcut Trick for Finding the Units Digits of Large Powers

Easy Way of finding the Units Digit of Large Powers | How to find the Units Digit of Large Powers| Trick to find the Unit Digits of Large Powers.

In Exam, you may find few questions based on finding the Units Digits of Large Powers. A typical example of such questions is listed below:

(a) Find the Units Place in  (785)98 + (342)33 + (986)67

(b) What will come in Units Place in  (983)85 -  (235)37

These questions can be time consuming for those students who are unaware of the fact that there is a shortcut method for solving such questions. Don't worry if you don't know the shortcut already because we are providing it today.
 

Finding the Unit Digit of Powers of 2

  1. First of all, divide the Power of 2 by 4.
  2. If you get any remainder, put it as the power of 2 and get the result using the below given table.
  3. If you don't get any remainder after dividing the power of 2 by 4, your answer will be (2)which always give 6 as the remainder
Power Unit Digit
(2)1 2
(2)2 4
(2)3 8
(2)4 6


Let's solve few Examples to make things clear.

(1) Find the Units Digit in (2)33
Sol -
Step-1:: Divide the power of 2 by 4. It means, divide 33 by 4.
Step-2: You get remainder 1.
Step-3: Since you have got 1 as a  remainder , put it as a power of 2 i.e (2)1.
Step-4: Have a look on table, (2)1=2. So, Answer will be 2


(2) Find the Unit Digit in (2)40
Sol -
Step-1:: Divide the power of 2 by 4. It means, divide 40 by 4.
Step-2: It's completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 2 i.e (2)4.
Step-4: Have a look on table, (2)4=6. So, Answer will be 6

 

Finding the Unit Digit of Powers of 3 (same approach)

  1. First of all, divide the Power of 3 by 4.
  2. If you get any remainder, put it as the power of 3 and get the result using the below given table.
  3. If you don't get any remainder after dividing the power of 3 by 4, your answer will be (3)which always give 1 as the remainder
Power Unit Digit
(3)1 3
(3)2 9
(3)3 7
(3)4 1


Let's solve few Examples to make things clear.

(1) Find the Units Digit in (3)33
Sol -
Step-1:: Divide the power of 3 by 4. It means, divide 33 by 4.
Step-2: You get remainder 1.
Step-3: Since you have got 1 as a  remainder , put it as a power of 3 i.e (3)1.
Step-4: Have a look on table, (3)1=3. So, Answer will be 3


(2) Find the Unit Digit in (3)32
Sol -
Step-1:: Divide the power of 3 by 4. It means, divide 32 by 4.
Step-2: It's completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 3 i.e (3)4.
Step-4: Have a look on table, (3)4=1. So, Answer will be 1
 

Finding the Unit Digit of Powers of 0,1,5,6

The unit digit of 0,1,5,6 always remains same i.e 0,1,5,6 respectively for every power.

 

Finding the Unit Digit of Powers of 4 & 9

In case of  4 & 9, if powers are Even, the result will be 6 & 4. However, when their powers are Odd, the result will be 1 & 9. The same is depicted below.

  • If the Power of 4 is Even, the result will be 6
  • If the Power of 4 is Odd, the result will be 4
  • If the Power of 9 is Even, the result will be  1
  • If the Power of 9 is Odd, the result will be 9.

For Example - 

  • (9)84 = 1
  • (9)21 = 9
  • (4)64 = 6
  • (4)63 = 4

 

Finding the Unit Digit of Powers of 7 (same approach)

  1. First of all, divide the Power of 7 by 4.
  2. If you get any remainder, put it as the power of 7 and get the result using the below given table.
  3. If you don't get any remainder after dividing the power of 7 by 4, your answer will be (7)which always give 1 as the remainder
Power Unit Digit
(7)1 7
(7)2 9
(7)3 3
(7)4 1


Let's solve few Examples to make things clear.

(1) Find the Units Digit in (7)34
Sol -
Step-1:: Divide the power of 7 by 4. It means, divide 34 by 4.
Step-2: You get remainder 2.
Step-3: Since you have got 2 as a  remainder , put it as a power of 7 i.e (7)2.
Step-4: Have a look on table, (7)2=9. So, Answer will be 9


(2) Find the Unit Digit in (7)84
Sol -
Step-1:: Divide the power of 7 by 4. It means, divide 84 by 4.
Step-2: It's completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 7 i.e (7)4.
Step-4: Have a look on table, (7)4=1. So, Answer will be 1

 

Finding the Unit Digit of Powers of 8 (same approach)

  1. First of all, divide the Power of 8 by 4.
  2. If you get any remainder, put it as the power of 8 and get the result using the below given table.
  3. If you don't get any remainder after dividing the power of 8 by 4, your answer will be (8)which always give 6 as the remainder
Power Unit Digit
(8)1 8
(8)2 4
(8)3 2
(8)4 6


Let's solve few Examples to make things clear.

(1) Find the Units Digit in (8)34
Sol -
Step-1:: Divide the power of 8 by 4. It means, divide 34 by 4.
Step-2: You get remainder 2.
Step-3: Since you have got 2 as a  remainder , put it as a power of 8 i.e (8)2.
Step-4: Have a look on table, (8)2=4. So, Answer will be 4


(2) Find the Unit Digit in (8)32
Sol -
Step-1:: Divide the power of 8 by 4. It means, divide 32 by 4.
Step-2: It's completely divisible by 4. It means, the remainder is 0.
Step-3: Since you have got nothing as a  remainder , put 4 as a power of 8 i.e (8)4.
Step-4: Have a look on table, (8)4=1. So, Answer will be 6


Now, you can easily solve questions based on finding the Unit's Digit of large powers. Lets try at least a few.

(a) Find the Units Place in  (785)98 + (342)33 + (986)67

Sol : 5 + 2 + 6 = 13 . So answer will be 3 .


(a) Find the Units Place in  (983)85 -  (235)37

Sol :  3 - 5 = 13 - 5 = 8  . So answer will be 8 . In this question, we have considered 3 as 13 because 3-5= -2 which is negative which is not possible.

The document Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) Notes | Study UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making - UPSC is a part of the UPSC Course UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making.
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