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Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) | Quantitative for GMAT PDF Download

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) | Quantitative for GMAT is a part of the GMAT Course Quantitative for GMAT.
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FAQs on Unit Digit Calculation Notes (How to Calculate Unit Digit within seconds) - Quantitative for GMAT

1. How do you calculate the unit digit within seconds?
Ans. To calculate the unit digit within seconds, you can follow these steps: 1. Write down the given number. 2. If the number has multiple digits, focus only on the unit digit. 3. Apply the appropriate mathematical operations (addition, subtraction, multiplication, or division) to the unit digit. 4. Keep performing the operations until you reach a single-digit number. 5. The final single-digit number obtained will be the unit digit of the original number.
2. What is the significance of the unit digit in calculations?
Ans. The unit digit plays a crucial role in calculations as it helps determine certain properties or patterns. It simplifies complex calculations by allowing us to focus on the last digit instead of the entire number. By analyzing the unit digit, we can identify patterns, divisibility rules, and make predictions about the outcomes of various mathematical operations.
3. Can the unit digit be zero?
Ans. Yes, the unit digit can be zero. If the given number ends with zero or is a multiple of 10, its unit digit will be zero. However, it is important to note that if a number ends with zero, it does not mean that its unit digit will always be zero. Other digits in the number may affect the unit digit calculation.
4. How can I quickly find the unit digit of large numbers?
Ans. To quickly find the unit digit of large numbers, you can follow these strategies: 1. Focus only on the unit digit of each number. 2. Identify any patterns or recurring sequences in the operations you need to perform. 3. Use the properties of unit digits, such as the cyclicity of certain numbers, to simplify calculations. 4. Break down complex numbers into smaller components and calculate their unit digits individually before combining the results.
5. Are there any shortcuts or tricks for calculating the unit digit?
Ans. Yes, there are several shortcuts and tricks you can use to calculate the unit digit efficiently: 1. Use the concept of cyclicity to identify repeating patterns in the unit digits of powers. 2. Memorize the unit digit values of common numbers and their powers. 3. Apply divisibility rules to quickly determine the unit digit of a quotient or product. 4. Break down the given number into simpler components, such as prime factors, and calculate the unit digit of each component separately before combining the results.
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