How can we use irrational numbers in math if we don’t know the full number?
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There’s two answers here:
**Arithmetic**: When you’re calculating something use traditional digits (1, 2, 3, etc), you don’t need to be perfectly precise.
Even NASA only needs about 15 digits of Pi to put a rover on Mars. It doesn’t take very many digits to have *basically* perfect precision.
**Mathematics**: For most irrational numbers, we do *know* the full number. We know how to calculate the exact number to any digit into infinity. We just cannot represent that full number in decimal form. This is a limitation of how we write numbers, not a limitation to how we *understand* numbers.
π (aka Pi) is the notation for the exactly precise number of Pi. You might lose precision when writing it out as digits (3.1415…). Losing precision doesn’t mean we don’t know the number.
It’s kind of like if you have to draw your own face. You *do know your face*. You recognize it, you would immediately recognize an imposter, even if it were very close to your face. But some methods of representing your face (a picture) are much more accurate than others (a drawing).
For many, many applications, you don’t need to have a decimal form of an irrational number in order to use it.
Here’s an easy example. I have Circle A with a radius of 1. I want to know what is the radius of a Circle B with a diameter exactly twice as big.
When I go through the math of that, I’ll find I don’t need a single digit of Pi. To double the circumference, I double the radius (Pi cancels out).
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