Number System || UNIT DIGIT (LESSON-3)

Summary

This YouTube video focuses on teaching viewers how to determine the unit digits of various numbers, a crucial skill for competitive exams such as railway and state exams. The host explains the concept of unit digits and provides several examples to help viewers understand how to find the last digit of the final answer in mathematical problems. The video emphasizes practicing examples, solving questions related to unit digits, and understanding the logic behind powers and remainders. Throughout, the host encourages viewers to subscribe to the channel for more educational content and exam tips.

Takeaways

• 😀 The video focuses on explaining the concept of unit digits in number systems, especially for competitive exams like railway and state exams.
• 😀 The importance of understanding unit digits for solving various problems in number systems is emphasized throughout the script.
• 😀 Several examples are provided to demonstrate how to find the unit digit of a number, such as 90, 12345, and others.
• 😀 Viewers are repeatedly encouraged to subscribe to the channel for more tutorials and updates on competitive exams.
• 😀 The script mentions solving basic level questions to help viewers get familiar with unit digits in numbers.
• 😀 A reminder is given to focus on the last digit of the number while solving problems and to apply this rule consistently.
• 😀 The video discusses examples involving powers of numbers (like 6^91), teaching how to identify the unit digit in such cases.
• 😀 Viewers are encouraged to practice solving problems from different model numbers to better understand the concept of unit digits.
• 😀 There are references to using a reminder system for determining unit digits, particularly in relation to modular arithmetic.
• 😀 The video ends by urging viewers to subscribe to the channel for future lessons and to stay updated with new educational content.

Q & A

What is the main topic discussed in the video?

The video focuses on understanding the number system, specifically the concept of unit digits and how to find the unit digit of a number, which is crucial for competitive exams such as railway and state exams.

Why is the unit digit important in solving number system problems?

The unit digit is important because it helps simplify calculations, especially when dealing with large numbers or powers of numbers. It is often the key to quickly finding the solution to a problem, especially in competitive exams.

What is the method to find the unit digit of a number?

To find the unit digit of a number, you simply focus on the last digit of the number. For example, if you are given the number 12345, the unit digit is 5.

Can you explain the process of calculating the unit digit of a power of a number?

To find the unit digit of a power, you look at the pattern in the unit digits of successive powers of the base number. For instance, for powers of 2, the unit digits cycle through 2, 4, 8, 6, and repeat every 4 powers.

What are some examples of base numbers and their unit digit patterns?

For example, the unit digit of powers of 2 follows a repeating pattern: 2, 4, 8, 6. Similarly, powers of 3 follow the pattern: 3, 9, 7, 1. Recognizing these patterns can help solve problems faster.

How do you solve problems involving the last digit of the sum of two numbers?

To find the last digit of the sum of two numbers, you simply add the unit digits of each number and take the unit digit of the result. For example, 56 + 77: the unit digits are 6 and 7, and their sum is 13, so the unit digit is 3.

What should be kept in mind when calculating the unit digit of large numbers or powers?

When calculating the unit digit of large numbers or powers, it’s important to identify and use the repeating pattern of unit digits for the base number. This can significantly reduce the complexity of calculations.

How do you find the unit digit of a large power like 2^100?

Since the unit digits of powers of 2 repeat every four numbers (2, 4, 8, 6), you divide the exponent (100) by 4 and take the remainder. For 2^100, the remainder is 0, so the unit digit is 6.

What is the importance of remembering unit digit patterns for competitive exams?

Remembering unit digit patterns allows candidates to quickly solve problems without performing full calculations, which is essential for saving time during exams and increasing accuracy.

Can you give an example of a complex problem involving unit digits, and how to solve it?

For example, finding the unit digit of 9^123. The unit digits of powers of 9 follow a repeating pattern: 9, 1. Since 123 divided by 2 gives a remainder of 1, the unit digit of 9^123 is 9.