X Tables
Maths History

Number systems around the world

Compare different ways humans have written numbers through history.

Quick answer

Different cultures around the world have used many different ways to write numbers, from simple marks on bones to complex symbols like Roman numerals and the Hindu-Arabic system we use today.

Learning outcome

By the end of this page, you will understand how different number systems work and why we use the one we do now. Success signs:
  • You can explain why we use our current number system
  • You can compare at least two different number systems
  • You can count using a simple ancient number system
  • You can find real-life examples of number systems in history

Why this matters

Understanding how numbers have changed over time helps you appreciate why we have the system we use today. It also shows how important maths is in human history and how people from all over the world have needed to count and measure things. When you know about ancient number systems, you can better understand how maths grew and why it's so useful in games, science, and everyday life.

How it works

Number systems are ways of writing numbers. They can be simple or complex. Ancient people needed numbers for:
  • Trading goods
  • Measuring land
  • Keeping track of time
  • Building structures
Different cultures used different methods:
  1. Simple marks or notches on bones or sticks
  2. Groups of objects like stones or shells
  3. Special symbols or letters
  4. Systems with place values (where position shows value)

Examples you can see

Let's look at some number systems from history: 1. Tally marks The oldest way to count was with marks on bones or sticks. Each mark meant one thing.
  • One mark = 1
  • Two marks = 2
  • Five marks = 5
This system was good for small numbers but hard to use for big numbers. 2. Roman numerals The Romans used letters to make numbers:
  • I = 1
  • V = 5
  • X = 10
  • L = 50
  • C = 100
  • D = 500
  • M = 1000
Numbers are made by adding or subtracting these letters:
  • VI = 6 (5 + 1)
  • IV = 4 (5 - 1)
  • IX = 9 (10 - 1)
3. Egyptian hieroglyphs Ancient Egyptians used pictures to show numbers:
  • A stick = 1
  • A heel bone = 10
  • A coil of rope = 100
  • A lotus flower = 1000
They wrote numbers by combining these symbols. 4. Hindu-Arabic numerals This is the system we use today:
  • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
It uses place value - the position of each digit shows its value. For example, in 234:
  • 2 is in the hundreds place (2 × 100 = 200)
  • 3 is in the tens place (3 × 10 = 30)
  • 4 is in the ones place (4 × 1 = 4)

Try it as a mini adventure

Adventure: The Ancient Market You are an ancient trader in a faraway land. You need to count your goods and pay for things using different number systems. Step 1: You have 12 oranges. Count them using tally marks.
  • |||| || = 12
Step 2: You have 15 apples. Count them using Roman numerals.
  • XV = 15
Step 3: You want to buy 30 pieces of cloth. The shopkeeper uses Egyptian numbers.
  • 30 pieces = |||| |||| |||| (three coils of rope)
Step 4: You have 247 coins. Count them using our modern system.
  • 247 = 2 hundreds + 4 tens + 7 ones
Step 5: Which system is easiest to use? Why?
  • Our modern system is easiest because we can write any number using just 10 symbols and place value

Common mistakes

  • Mistake: Thinking Roman numerals are just letters
    • Why it happens: Children may confuse letters with numbers
    • Fix: Remember that Roman numerals are combinations of letters that show specific values, not just random letters
  • Mistake: Not understanding that our modern system uses place value
    • Why it happens: Children may see numbers as just symbols without understanding their position
    • Fix: Practice with base-10 blocks or drawings showing hundreds, tens, and ones
  • Mistake: Mixing up Roman numeral symbols
    • Why it happens: Similar-looking symbols like I, V, X, L, C, D, M can confuse children
    • Fix: Use flashcards or games to practice each symbol and its value
  • Mistake: Believing ancient systems were more complicated than ours
    • Why it happens: Children may think complex-looking symbols mean more difficult maths
    • Fix: Show that simple systems like tally marks were very useful for basic counting

Parent and carer guide

Help your child understand number systems by:
  • Playing a game where you count objects using different methods (tally marks, Roman numerals, base-10 blocks)
  • Looking at old clocks or monuments that use Roman numerals
  • Discussing why we use our modern system (it's easier to write and calculate with)
  • Using everyday examples like counting coins or measuring ingredients
  • Encouraging them to make their own number system using shapes or symbols
In just 5-10 minutes, you can:
  1. Count together using tally marks
  2. Write numbers 1-20 in Roman numerals
  3. Discuss why our number system works well
  4. Draw simple ancient number symbols
Remember: This is about understanding history, not memorizing facts. Focus on the concepts and connections between systems.

Practice questions

  1. What does the Roman numeral IX mean?
    • Answer: 9
  2. How would you write 16 in Roman numerals?
    • Answer: XVI
  3. What is the value of the digit 5 in the number 532?
    • Answer: 500 (five hundreds)
  4. How many tally marks would you need to show 13?
    • Answer: 13 marks
  5. What is the difference between Egyptian hieroglyphs and our modern system?
    • Answer: Egyptian used pictures for numbers, while we use symbols with place value

FAQ

What is a number system?

A number system is a way of writing numbers using symbols or methods. Different cultures have used different systems throughout history.

Why do we use the Hindu-Arabic system?

We use this system because it's very efficient. It uses only 10 symbols (0-9) and place value, which makes it easy to write and calculate with large numbers.

Are Roman numerals still used today?

Yes! We still use Roman numerals for things like clock faces, movie credits, book chapters, and page numbers in some books.

How did ancient people count before numbers?

They used their fingers, toes, stones, shells, notches on bones, and other physical objects to keep track of quantities.

What was the biggest advantage of the Hindu-Arabic system?

The biggest advantage was the introduction of zero and place value. This made it much easier to write and work with large numbers than earlier systems.