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FAQs on Let's Learn: Representation of a Number - Mathematics (Maths Mela) Class 5 - New NCERT
| 1. What is the representation of numbers in different number systems? |  |
Ans.Numbers can be represented in various number systems, including the decimal system (base 10), binary system (base 2), octal system (base 8), and hexadecimal system (base 16). In the decimal system, numbers are represented using ten digits (0-9). The binary system uses two digits (0 and 1), which is foundational in computing. The octal system uses digits from 0 to 7, while the hexadecimal system uses digits from 0 to 9 and letters A to F to represent values from 10 to 15. Each system has its unique applications and importance in mathematics and technology.
| 2. How do you convert a decimal number to binary? | |
Ans.To convert a decimal number to binary, you can use the method of successive division by 2. You divide the decimal number by 2, recording the quotient and the remainder. You continue dividing the quotient by 2 until the quotient becomes 0. The binary representation is then obtained by reading the remainders in reverse order. For example, to convert the decimal number 10 to binary, you would divide: 10 ÷ 2 = 5 (remainder 0), 5 ÷ 2 = 2 (remainder 1), 2 ÷ 2 = 1 (remainder 0), and 1 ÷ 2 = 0 (remainder 1). Reading the remainders from bottom to top, 10 in decimal equals 1010 in binary.
| 3. What are the advantages of using the binary number system? | |
Ans.The binary number system is advantageous primarily due to its simplicity and efficiency in electronic circuits. Since it only uses two digits (0 and 1), it aligns perfectly with the on-off states of electronic switches, which makes binary ideal for digital systems and computers. This simplicity leads to more reliable data processing and storage. Additionally, binary arithmetic is straightforward, making it easier to perform operations like addition and subtraction in computing.
| 4. Can you explain the place value system in the decimal number system? | |
Ans.The place value system in the decimal number system is based on the position of digits in a number. Each digit has a value that is determined by its position, which is a power of 10. For example, in the number 345, the digit 3 is in the hundreds place (3 x 10² = 300), the digit 4 is in the tens place (4 x 10¹ = 40), and the digit 5 is in the units place (5 x 10⁰ = 5). Thus, the total value is 300 + 40 + 5 = 345. This system allows for the representation of large numbers efficiently.
| 5. What is the importance of understanding number representation in mathematics? | |
Ans.Understanding number representation is vital in mathematics as it forms the foundation for various mathematical concepts and operations. It helps students grasp the concept of quantities, perform calculations, and understand relationships between numbers. Additionally, knowledge of different number systems is essential in computer science, coding, and data representation, making it a crucial skill in today's technology-driven world. By mastering number representation, students can enhance their problem-solving abilities and mathematical reasoning.
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Sep 08, 2025
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