The Topic:
Number Systems

Easier - A number system is a way of counting things. It's a way of identifying the quantity of something.
Harder - A number system is the set of symbols used to express quantities as the basis for counting, determining order, comparing amounts, performing calculations, and representing value. It is the set of characters and mathematical rules that are used to represent a number. Examples include the Arabic, Babylonian, Chinese, Egyptian, Greek, Mayan, and Roman number systems. The ISBN and Dewey Decimal System are examples of number systems used in libraries. Social Security even has a number system.
Development of Counting Systems and Notations by M.I. Woodcock
This module has been produced as a distance-learning package. It is intended that the student should read through the notes provided and use the reading list and other History of Mathematics links to answer further questions.
Links to Information on Number Systems by S. Alejandre from The Math Forum
This site connects to websites on Arabic, Babylonian, Chinese, Egyptian, Greek, Mayan, and Roman number systems.
Related Website:
2) Numbers and Number Theory Index from University of St. Andrews, Scotland
See additional sites below in the Ancient Number Systems
Number System from Kid's Online Resources, College of the Redwoods
Designed for beginning computer students, this site introduces binary, decimal, hexadecimal systems and includes definitions and conversions.
Related Websites:
2) Conversion Between Different Number Systems
3) Data Structures And Number Systems
4) Digital Number System
5) Number Systems and Codes
Wise Up! We Use Numbers All the Time from British Broadcasting Corporation (BBC)
The activity at this website is a review of our base 10 number system. You can follow this up with a fact sheet and an online test.
After visiting several of the websites for number systems, continue your explorations by completing one or more of these activities.
Complete A Number Systems WebQuest. Adapt or follow the procedures found at one of the following webQuest sites:
1) Creative Encounter of the Numerical Kind (Grades 6-8) by A. Gabbard
2) Dewey Decimal System (Grades 4-6)
3) Discovering Number Systems of Ancient Civilizations (Grades 9-12) by J. Grant
4) Number Systems (Grade 3-4) by R. Encarnacion
Practice Your Roman Numerals Math. Go to the interactive Java site, Roman Numerals Math by O. Lawrence and test your skill. You also may enjoy the Roman Numeral Game.
Learn To Use An Abacus. After visiting several of the websites on the Abacus, use the online Interactive Abacus Tutor by S. Chandran and D.A. Bagley's. Keyboard in a value and see the result.
Test Your Dewey Decimal Classification Knowledge. Try the online quiz at Do the Dewey! from the Middleton Thrall Library, NY. Choose the level you want and see how you do.
Convert Numbers To Different Base Systems. Use the online Number System Conversion Tool to practice converting between different number systems, using bases 2-16. After you understand the concepts and their application, you then could try the Number System Conversion Quiz.
Compare and Contrast Two Different Number Systems. Pick two number systems. Then identify how the two systems are alike and different. Present you findings in a visual display.
Websites By Kids For Kids
Abacus Online (2000 ThinkQuest Internet Challenge)
This site explores the abacus, particularly the Chinese (2/5) styled abacus or suan puan, and contains information on its history, tutorials on how to use it, and more.
Do We Really Know Dewey? (Silver Award, 1999 ThinkQuest Junior Project)
This is a website created to teach kids about the Dewey Decimal System. There are several levels, so it could be used with different age groups. For example, the "Alien" story and the "Pre-Dew Review" sections could be used with earlier elementary levels. Middle grades could also learn a lot from the "Let's Dew It" section. For those students who are ready for more challenging information, there is "Let's Dew it Again".
Elementary Number Theory (2001 ThinkQuest Internet Challenge)
This is a site introducing elementary number theory, including prime number, divisibility and some Java games
Integers (2000 ThinkQuest Internet Challenge)
This site investigates the development of number systems.
Simply Number Sense! (1998 ThinkQuest Internet Challenge)
Have you hit the brick wall of confusion in mathematics? Do your numbers have so many places that you don't know what to call them? Does the thought of decimals, fractions, and percentages curl your hair? Brush up with this tutorial.
Ancient Number Systems
Babylonian Numerals by J.J. O'Connor and E.F. Robertson
The Babylonians inherited ideas from the Sumerians and from the Akkadians. From the number systems of these earlier peoples came the base of 60, that is the sexagesimal system. Yet neither the Sumerian nor the Akkadian system was a positional system, and this advance by the Babylonians was undoubtedly their greatest achievement in terms of developing the number system.
Related Websites:
2) Counting in Babylon by M. Fowler
3) Cuneiform Numbers by D.J. Melville
4) Sumerian and Babylonian Numerals by M.I.Woodcock
Chinese Numbers
While China has for many uses adopted the Arabic numeral system familiar around the world, it also still uses its native Chinese character number system. The Chinese system is also a base-10 system, but has important differences in the way the numbers are represented.
Egyptian Numerals from History of Mathematics in Africa
The Egyptian numbering system was also based on units of 10, but instead of relying on the position of numbers to define their value, the Egyptians used different images to represent different units of 10.
Related Websites:
2) Egyptian Number Systems
3) Egyptian Numerals by M.I. Woodcock
4) Hieroglyphic Numbers
Hindu-Arabic Numerals by M.I. Woodcock
The Hindu system is a pure place value system, that is why you need a zero. Only the Hindus within the context of Indo-European civilizations have consistently used a zero.
Maya Mathematics
Instead of ten digits like we have today, the Maya used a base number of 20. (Base 20 is vigesimal.) They also used a system of bar and dot as "shorthand" for counting.
Related Websites:
2) Mayan Math by K.M. Strom
3) Mayan Numbers
4) Mayan Number System by S. Jimenez
5) Mayan Numerals from History of Mathematics in Americas
6) Mayan Numerical System
Roman Numerals 101 by O. Lawrence
The Romans counted according to decimal mathematics, just like we do, but with a different style of writing. It is useful to know this method of writing because we still run across these numbers today.
Related Website:
2) Roman Numeration from Rome's Imperial Forums
More Websites on Number Systems
Abacus: The Art of Calculating with Beads
The abacus is a mechanical aid used for counting. Addition, subtraction, division and multiplication can be performed on a standard abacus.
Related Website:
2) Abacus in Various Number Systems
Base Valued Numbers
The basic rules for a formalized base numbering system involve ordering items, grouping ordered items and then expressing the groups and items in a consistent way. The way it represents the different groups gives the numbering system an order of magnitude.
Binary - How Does It Work? by K. Redshaw
It's not so difficult! Binary numbers use the same rules as decimal - the value of any digit always depends on its position in the whole number. It all gets down to bases. Decimal uses base ten and Binary, on the other hand, uses base two.
Related Website:
2) Binary Number System
First Place-Value Number System from A History of Computers
The decimal system is a place-value system, which means that the value of a particular digit depends both on the digit itself and on its position within the number.
Related Section:
2) Invention of the Abacus
Numbering Systems and Place Values
Learn about about large numbers and their place values including ones up to trillions, tenths down to trillionths; the American Numbering System; Googol and Googolplex; and the British Numbering System.
Numeric Systems
This website defines number systems, then provides information about binary and the hexadecimal system.
Place Value to 1,000: What Is It? from MathSteps
Place value is the basis of our entire number system. A place value system is one in which the position of a digit in a number determines its value.
Related Website:
2) All About Place Values by J.Banfill from AAA Math
Understanding Decimal, Binary, Hexadecimal from Exploring MIDI
This page summarizes three basic numbering systems: decimal, binary, and hexadecimal.
Related Websites:
2) Binary/Octal/Decimal/Hexadecimal Conversion
3) Counting: Base 6, 12, 16 by S. Asplund from The Math Forum
4) Hexadecimal Number System by E. Østergaard
Understanding Call Numbers
Have you ever wondered how library books are assigned their places on the shelves? Did you know that the call number -- the number placed on the spine of the book -- is a code which provides valuable information about the book? This page will provide an introduction to understanding and using Library of Congress Classification call numbers.
Related Websites:
2) Dewey Decimal Classification
3) Dewey Decimal Classification System
4) Dewey Decimal System
5) Dewey Decimal System
6) Let's Do Dewey
Websites For Teachers
MacCandy Factory Microworlds
The objective of this first program (Download software at this site) is to engage students in the activities of packing and unpacking to build a sense of place value and ten as a composite unit.
Place Value (Grades 1-4) from Mid-continent Research for Education & Learning (McREL)
Here is a collection of lesson plans and activities for learning about place value.
Related Lesson Plans:
2) Fictional History of Place Value by B.B. Jarrow
3) Hands-on Role Play Activity: Counting the Rice (Grades 2-8)
4) Place Value for Elementary Students (Involving movement, music, and reflection) from Southwest Educational Development Laboratory
5) Place Value Game (Grades 1-8) by T. Sayre
Primary Understanding and Use of Place Value by E. Brzozowski from Hanson Park School
This lesson examines some of the people that have contributed to the development of modern arithmetic (number systems); to provide a better understanding of our base 10 number system and its application to real life problems.
Socratic Method: Teaching by Asking Instead of by Telling by R. Garlikov
The is a transcript of a teaching experiment, using the Socratic method, with a regular third grade class in a suburban elementary school. The experiment was to see whether I could teach these students binary arithmetic (arithmetic using only two numbers, 0 and 1) only by asking them questions.
place value
order of magnitude
golden ratio
negative number
positive number
natural number
decimal number system
prime number
base 10
"take a number"
number system
Created by Annette Lamb and Larry Johnson, 7/02.