This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses many of aspects of whole numbers, including the Hindu-Arabic numeration system, the base ten positional number system, and the graphing of whole numbers. By the end of this module students should be able to: know the difference between numbers and numerals, know why our number system is called the Hindu-Arabic numeration system, understand the base ten positional number system, and identify and graph whole numbers.
Section overview
- Numbers and Numerals
- The Hindu-Arabic Numeration System
- The Base Ten Positional Number System
- Whole Numbers
- Graphing Whole Numbers
Numbers and numerals
We begin our study of introductory mathematics by examining its most basic building block, the
number .
Number
A
number is a concept. It exists only in the mind.
The earliest concept of a number was a thought that allowed people to mentally picture the size of some collection of objects. To write down the number being conceptualized, a
numeral is used.
Numeral
A
numeral is a symbol that represents a number.
In common usage today we do not distinguish between a number and a numeral. In our study of introductory mathematics, we will follow this common usage.
Sample set a
The following are numerals. In each case, the first represents the number four, the second represents the number one hundred twenty-three, and the third, the number one thousand five. These numbers are represented in different ways.
- Hindu-Arabic numerals
4, 123, 1005
- Roman numerals
IV, CXXIII, MV
- Egyptian numerals
Practice set a
Do the phrases "four," "one hundred twenty-three," and "one thousand five" qualify as numerals? Yes or no?
Yes. Letters are symbols. Taken as a collection (a written word), they represent a number.
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The hindu-arabic numeration system
Hindu-arabic numeration system
Our society uses the
Hindu-Arabic numeration system . This system of numeration began shortly before the third century when the Hindus invented the numerals
0 1 2 3 4 5 6 7 8 9
Leonardo fibonacci
About a thousand years later, in the thirteenth century, a mathematician named Leonardo Fibonacci of Pisa introduced the system into Europe. It was then popularized by the Arabs. Thus, the name, Hindu-Arabic numeration system.
The base ten positional number system
Digits
The Hindu-Arabic numerals 0 1 2 3 4 5 6 7 8 9 are called
digits . We can form any number in the number system by selecting one or more digits and placing them in certain positions. Each position has a particular value. The Hindu mathematician who devised the system about A.D. 500 stated that "from place to place each is ten times the preceding."
Base ten positional systems
It is for this reason that our number system is called a
positional number system with
base ten .
Commas
When numbers are composed of more than three digits,
commas are sometimes used to separate the digits into groups of three.
Periods
These groups of three are called
periods and they greatly simplify reading numbers.
In the Hindu-Arabic numeration system, a period has a value assigned to each or its three positions, and the values are the same for each period. The position values are
