Why are there no infinite left-sided decimal expansions?

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. M...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical gazette 2021-03, Vol.105 (562), p.78-86
Main Author: Paseau, A. C.
Format: Article
Language:English
Subjects:
Integers
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0025-5572
2056-6328
DOI:10.1017/mag.2021.10