Let’s use a real-world hero: pizza. A 10-inch pizza has a circumference of about 31.4 inches. That “about” is key. The exact number is 10 times pi, and pi is the most famous irrational number of all.
Pi (π) is roughly 3.14159… and it just keeps going, with no end in sight. You can approximate pi with the fraction 22/7, but that’s 3.142857…, which is close, but not precise. Try cutting a pizza with that tiny error—your slices won’t fit the box perfectly.
This means no matter how sharp your knife or fine your measuring tape, you can never write the exact circumference of a perfect circle as a simple fraction. It’s a little humbling, isn’t it? Even the universe refuses to be pinned down by a neat ratio.
Why You Should Care (Yes, Really)
You might think, “Great, so I can’t perfectly slice a pie. I’ll survive.” And you will! But these numbers are hiding in places you love. Have you ever folded a piece of paper in half, and then in half again, trying to make a perfect right triangle?
The diagonal of that triangle is probably related to the square root of 2 (√2), another irrational number. It shows up in every square and every rectangle you see—your phone, your TV, your book. √2 is about 1.41421356… and it never repeats.
Why Can’t Irrational Numbers Be Written as Fractions? | NCERT Class 9
Sure, your TV works fine without thinking about it. But when you zoom in on a photo or resize a window, your computer’s software uses these irrational numbers to keep the image crisp and proportional. If it tried to use a simple fraction, the picture would get distorted.
