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?

In: 0

Answer 1

Try it with fractions instead of decimals. Squaring anything less than a whole number you are multiplying a fraction by a fraction, which will result in a smaller number.

For example:

1/4 * 1/4

You are finding a quarter of a quarter, which is 1/16. The denominator is getting larger but the numerator remains the same.