Questions and Answers
What is the primary purpose of using numbers?
To count and make calculations
What is the difference between a number and a numeral?
A number is a value, while a numeral is a symbol
What is the Lebombo Bone an example of?
An ancient numeral system
What is the Base-10 Numeral System?
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What is the Roman Numeral System?
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What is the significance of the number 29 in the context of the Lebombo Bone?
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What is the purpose of a numeral?
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What is the difference between the number 4 and the numeral IV?
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Why are numbers and numerals often confused?
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What is the quantity represented by the marbles in the example?
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What does the subscript DEC stand for in the notation for numbers in Base10?
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What determines the value of each digit in the Base10 Number System?
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Why is it important to denote the numeral with its proper subscript when working with multiple number systems?
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What is the total value of the numeral 4862 in Base10?
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What is the subscript notation for Base16?
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What is the place value of the first digit in the numeral 4862 in Base10?
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What is the base number of the system that uses the subscript OCT?
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What is the value of each digit in the Base10 Number System determined by?
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What is unique to the Base10 Number System?
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What is the purpose of using subscripts in number systems?
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What is a number system?
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Why do you think Base-10 has become the most preferred number system?
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What is the base of a number system that uses only two different characters?
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What is the purpose of a base in a number system?
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What is the value of the rightmost digit in a base-10 number system?
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How do you create different numeric values in a base-10 number system?
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What is the decimal number system also known as?
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Why are old number systems still used?
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What is the role of the base in a number system?
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How many different base number systems will be used in this course?
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Study Notes
Numbers and Numerals
- Numbers are values representing a particular quantity for counting, calculation, or showing order.
- Numbers can be expressed in words, symbols, or figures.
- People have used numbers since ancient times, even before formal writing.
Numbers Versus Numerals
- A number is the same regardless of the numeral used to describe it.
- A numeral is a name given to a number to identify it.
- The same number can be represented by different numerals (e.g., 4, IV, IIII).
Number Systems
- A number system is an organized group of symbols that represent numbers in a consistent manner.
- Number systems do not change over time, unlike languages.
- Old number systems are still used, even when new ones are created.
Base Number System
- A base number system is a system that uses a specific number of digits or combination of digits and letters to represent numbers.
- The base of a number system determines the number of characters used.
- Examples of base number systems: Binary (Base-2), Octal (Base-8), Decimal (Base-10), Hexadecimal (Base-16).
Base-10 Number System
- Base-10 is the most commonly used number system.
- It uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- The base-10 system is also known as the Decimal System.
- The base-10 system is used because it is natural for humans, with 10 fingers.
Understanding Base-10
- The base-10 system works by combining different combinations of the 10 digits to create different numeric values.
- Each digit in a base-10 number has a place value, which is multiplied by 10 to a power to create the total value.
- The notation for numbers in base-10 is denoted by a DEC (decimal) subscript after the numeral.
Converting Between Number Systems
- The digits of the base-10 system can be used in other systems, but they represent different values.
- It is important to denote the numeral with its proper subscript when working with multiple number systems.
- Subscript notation for each base number system: BIN (Base-2), OCT (Base-8), DEC (Base-10), HEX (Base-16).
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