How can we use irrational numbers in math if we don’t know the full number?
In: 232
Two things. First, “1.1616” and “√2” and “*e*” are all perfectly valid symbols for real numbers. You’re bothered that *you* can’t recite the number in its entirety, or that it’s not an Arabic numeral, but the choice of symbol and number of digits doesn’t make a number less real. It only affects how you express them in math problems. “3 pi” is just as valid as 3*e* or 300.
Second, things we measure have a significant number of digits, a number of decimal places that we “trust” depending on the tools we measure with. ALL measurements are rounded. All of them. You have “1” ruler, because that’s counted. But your ruler is approximately 12 inches, rounded up from 11.9-something inches. That’s measured.
Let’s say we want to know the circumference of a circle, and the formula is “diameter x π (pi)”. You might measure a circle to be 3.5 inches in diameter with a ruler. Your answer has to be rounded to 2 digits. A physicist with a laser circle-ometer might measure it as 3.4779236 inches. That answer will be rounded to 8 digits. Each of you has some instrument where the number’s on the left side of the line but not exactly on the line, and you’re both rounding. So it doesn’t matter that pi goes on forever; you can’t measure the width of a circle accurately enough to need forever digits. But when you grow up and invent a circle-ometer that can measure to trillionths of an inch, there will be digits of pi waiting for you to use them.
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