Babylonian base 60

Quick answer

The Babylonians used a base-60 number system, which is why we still use 60 minutes in an hour, 60 seconds in a minute, and 360 degrees in a circle today.

Learning outcome

By the end of this page, you will understand how the ancient Babylonians counted in base-60 and how this system still affects our daily lives with time and angles.

• You can explain why there are 60 seconds in a minute
• You can show how to count in base-60 using simple groups
• You can connect base-60 to real-life things like clocks and circles
• You can imagine how ancient people might have used this counting system

Why this matters

Learning about the Babylonian base-60 system helps you understand why we measure time and angles the way we do. It shows how ancient maths is still useful today. You might be surprised to find that your phone, your watch, and even your math lessons are connected to ancient Babylonian counting!

How it works

The Babylonians used a base-60 system, which means they counted in groups of 60. Just like we count in groups of 10 (our base-10 system), they counted in groups of 60. Let's imagine how this worked:

1. They used special symbols to represent numbers
2. They wrote numbers using a place value system, like our ones, tens, hundreds
3. They used two symbols: one for 1 and one for 10
4. They could write numbers like 60, 120, 180, 240, and so on

Imagine if you had 60 marbles. You would have one group of 60 marbles. If you had 120 marbles, that's two groups of 60. This is how they thought about numbers!

Examples you can see

Let's look at how the Babylonians might have counted using their base-60 system:

Here's a fun way to imagine it:

• Think of 60 as one big group
• Think of 120 as two big groups
• Think of 180 as three big groups
• Think of 240 as four big groups

Try it as a mini adventure

Imagine you're an ancient Babylonian living in a time before clocks! You need to count how long your day lasts.

Your adventure has 4 steps:

1. First, you count 60 small stones to represent one hour
2. Then, you collect 60 more stones to make 120 stones (two hours)
3. Next, you count 60 more stones to make 180 stones (three hours)
4. Finally, you collect 60 more stones to make 240 stones (four hours)

Now, imagine you have 240 stones. How many hours did you count?

Let's do a quick check: 240 ÷ 60 = 4 hours

You've discovered that 240 stones equal 4 hours in Babylonian counting!

Common mistakes

• Mistake: Thinking that base-60 means 60 groups of 10
  Why it happens: Confusing base-60 with base-10
  Fix: Remember that in base-60, each group is 60, not 10
• Mistake: Adding numbers incorrectly in base-60
  Why it happens: Not understanding place value
  Fix: Remember that 60 ones make one group of 60
• Mistake: Thinking the Babylonians used the same symbols as we do
  Why it happens: Mixing up ancient and modern systems
  Fix: The Babylonians used special symbols and were very creative with their counting

Parent and carer guide

Helping your child understand base-60 can be fun and educational:

• Use physical objects like counters or coins to show groups of 60
• Ask your child to imagine how many groups of 60 they could make with 120 items
• Point out how we still use base-60 in time and angles every day
• Encourage them to think about how counting in 60s might be easier for some things
• Don't worry if they get confused at first - it's a big concept to understand

Ask questions like:

• How many minutes are in an hour?
• How many degrees are in a full circle?
• Can you think of other things that come in groups of 60?

Practice questions

1. How many minutes are in 3 hours?
   Answer: 180 minutes
2. How many seconds are in 2 minutes?
   Answer: 120 seconds
3. How many degrees are in a full circle?
   Answer: 360 degrees
4. If you have 240 stones, how many groups of 60 is that?
   Answer: 4 groups
5. How many hours are in 360 minutes?
   Answer: 6 hours
6. How many degrees are in half a circle?
   Answer: 180 degrees
7. How many seconds are in 5 minutes?
   Answer: 300 seconds
8. How many groups of 60 make 420?
   Answer: 7 groups
9. How many minutes are in a quarter of an hour?
   Answer: 15 minutes
10. How many degrees are in a right angle?
    Answer: 90 degrees

FAQ

Why did the Babylonians use base-60?

The Babylonians chose base-60 because it's a very useful number. It can be divided evenly by many smaller numbers: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. This made their maths easier for trade and astronomy.

How is base-60 still used today?

We still use base-60 in measuring time (minutes and seconds) and angles (degrees). These systems come directly from the Babylonian counting system.

Can you count in base-60 like the Babylonians?

Yes! You can imagine counting in groups of 60. For example, 60 would be one group, 120 would be two groups, 180 would be three groups, and so on.

What makes base-60 special compared to other numbers?

Base-60 is special because it has many factors. This means it's easy to split into equal parts, which is great for sharing, time, and measurements.

Are there any other ancient number systems?

Yes! The Egyptians used base-10, the Romans used base-10 but with letters, and the Mayans used base-20. Each system had its own special way of counting and writing numbers.