What is the base of the Decimal Number System?a)2b)8c)10d)16Correct an...
The base of the Decimal Number System is 10, and it consists of ten digits from 0 to 9.
What is the base of the Decimal Number System?a)2b)8c)10d)16Correct an...
Understanding the Decimal Number System
The Decimal Number System is one of the most widely used numerical systems in everyday life. Here’s a detailed explanation of why its base is 10.
What is a Base?
- The base of a number system indicates how many unique digits, including zero, are used to represent numbers.
- For example, in a base-2 (binary) system, there are 2 digits: 0 and 1. In a base-16 (hexadecimal) system, there are 16 digits: 0-9 and A-F.
Decimal System Basics
- The Decimal Number System is also known as the base-10 system.
- It employs ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- Each position in a decimal number represents a power of 10.
Why Base 10?
- The reason we use base-10 is largely historical and practical.
- It is believed that humans originally counted using their fingers, leading to the adoption of ten as a natural base.
- In terms of calculations, base-10 is user-friendly and intuitive for most mathematical operations.
Examples of Decimal Representation
- The number 345 in the decimal system can be broken down as:
- 3 × 10² + 4 × 10¹ + 5 × 10⁰
- This illustrates how each digit’s position corresponds to a power of 10.
Conclusion
- Therefore, the correct answer to the question is option 'C' because the Decimal Number System is fundamentally based on the number 10.
- Understanding the base allows for better comprehension of how numbers are structured and calculated in our everyday lives.
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