Why are there no infinite left-sided decimal expansions?

Extract

It was my nine-year-old daughter who got me interested in the title question. As she appreciates, multiplying an integer by a power of 10 is a cinch. To multiply 34 by 100, simply add two zeros at the end: 34 × 100 = 3400. Dividing 3400 by 100 is the reverse process: remove two zeros to obtain 34. More generally, to multiply an integer by 10^N, for non-negative N, add N zeros to the end of its decimal notation, and to divide an integer by 10^N remove N zeros from its end — so long as it has them. Easy-peasy; my daughter knows all that.