2 squared is 4, which is more than 2. However, 0.2 squared is 0.04, which is less than 0.2. Can someone explain this apparent contradiction where a number between 0 and 1 squared becomes less than the original number but everything else (more than 1) becomes more?

Question

And I understand for example if I’m talking about meters, it’ll become square meters so the comparison is not apples to apples anymore. But in situations where there is no unit (for example, a math equation where you need to find x, whatever X is), why is this not contradictory?

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Answer 1

Squaring a number is essentially multiplying that number by itself. So, this not a squaring issue, but more of a multiplication issue. Whenever you multiply by between 0 and 1, you get a smaller number.

When you multiply a whole number by a whole number, you get a bigger whole number. When you multiply a fraction by a fraction, you get a bigger fraction. However, a bigger fraction is technically a smaller number. 0.5 x 0.5 is 0.25. 0.25 is more fractured of a number than 0.5, but that makes it numerically less. Or in fraction form, 1/2 x 1/2 = 1/4. In this case, then numerator of the fraction become larger. However, larger numerator create a number of lower value.

It makes sense in the real life too. Let’s say you have half a pie. John then gets half of that half, so what does John get? That’s a quarter. By multiplying a half by a half, you have less than half.