Basics of Ancient Number Systems

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: What is an Absolute Value?

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:04 The Earliest Number Systems
  • 0:52 Babylonian Number System
  • 2:03 Roman Number System
  • 3:10 Mayan Number System
  • 3:37 Hindu-Arabic Number System
  • 4:21 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

From simple tally marks on a stick to complex written number systems that could be used to perform many types of calculations, people in the ancient world developed and used a wide variety of number systems. In this lesson, learn how ancient number systems were developed and used.

The Earliest Number Systems

For many thousands of years, people have counted things using their fingers and toes. At least 25,000 years ago, people also began making tally marks, marks on a stick or stone tablet to record numbers.

Tally marks are still used today by many people, maybe even you! You probably have used tally marks to keep up with the score of a game or count votes. Most tally mark systems have some way to represent multiples, usually of five or ten, by placing a slash or other marker through the earlier marks. This makes it easy to see how many marks you have. This simple number system was sufficient for many thousands of years and is still used in many situations, but it is difficult to record large numbers or perform complex mathematical operations using only tally marks.

Babylonian Number System

Approximately 5,000 years ago, one of the first written number systems arose in Babylon, which used a base of 60. Number systems with a base of 60 are called sexagesimal. For numbers less than 60, the Babylonians used a base-10 system. All of the Babylonian numbers could be written by combining just two symbols, as compared to the ten different symbols we use to represent numbers today.

The Babylonian system came from earlier Sumerian and Akkadian number systems, which were also sexagesimal. The Babylonians improved on earlier systems, however, by developing a positional system, in which the same symbol could be used to represent different orders of magnitude, depending on where it was located in the number. This was a major achievement that had not been done before. Our number system today is positional, as well. The same symbol, for example, 1, can be used to represent 1, 10, or 100 depending on where it is located.

You might be surprised to learn that even though it was developed thousands of years ago, we still use the Babylonian base-60 number system in some ways today. For example, there are 60 seconds in a minute and 360 degrees (or 6 times 60) in a circle.

Roman Number System

The Roman number system was in used in ancient Rome and in most of Europe for many years after the end of the Roman empire. In some situations, Roman numerals are still used today throughout the world.

The Roman number system was based on seven symbols that could be arranged to represent any positive number. The Roman number system did not include zero or negative numbers, and most historians believe that it derived from a primitive system of tally marks. The seven roman numeral symbols had the following values:

I - is one

V - is five

X - is ten

L - is fifty

C - is one hundred

D - five hundred, and

M - one thousand

The Roman number system was not positional like the Babylonian system, so the value of each symbol was simply added together to get the total value. For example, the Roman number MMDLXXII represents the number 1000 + 1000 + 500 + 50 + 10 + 10 + 1 + 1, which is 2,572 using modern notation.

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account