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What is an Irrational Number?


An Irrational Number is a number that goes on forever and never repeats. You can’t write it as a simple fraction like 1/2 or 3/4. It’s wild, endless, and full of mystery!

The most famous irrational number is π (pi). You’ve probably heard of it in circles:

12 ÷ 3 = 4 cookies each!

π ≈ 3.14159265… and it keeps going!

No pattern, no repeat — just digits forever.

Another example is the square root of 2 (√2). Try putting that into a fraction — you can’t! Its decimal also goes on and on with no repeating pattern.


How Do You Know It’s Irrational?

If a number can’t be written as a simple fraction, it’s irrational.

If the decimal never ends and never repeats, it’s irrational.

Try This Game with a Teacher:

"Rational or Irrational?" Detective

1️⃣ Your teacher writes a number on a card: 1.5, √2, π, 5/8, 0.333…

2️⃣ You guess: rational (can be written as a fraction) or irrational.

3️⃣ Talk through the answer together. Why is it one or the other?

Even though irrational numbers can’t be written neatly, they’re super important in math and science. They help us measure curves, design circles, and even build buildings! They’re like math’s endless explorers.


Practice Time!

Test your skills and have fun with our Missing Numbers Quiz! 🎯