Proof of a different kind of infinity - Fractional Infinity

When you divide one by a million, you get a million millionths.
Now, one of those Millionths; is it far from zero?
Well then try dividing 1 by a trillion. You get a trillion trillionths.
A trillionth is smaller than a millionth so surely that must be closer to zero, right?
But then you divide one by say quadrillion and get quadrillion quadrillionths.
Is a quadrillionth any closer to zero than the trillionth or the millionth?

You see, within 1 there is an infinity. 1 can be infinitely divided into smaller and smaller fractions and however small you make the fractions you will never come close to zero, there will always be smaller fractions you can make.