Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T15:06:01.301Z Has data issue: false hasContentIssue false

Why are there no infinite left-sided decimal expansions?

Published online by Cambridge University Press:  17 February 2021

A. C. Paseau*
Affiliation:
Wadham College, Oxford OX1 3PN e-mail: [email protected]

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 10N, for non-negative N, add N zeros to the end of its decimal notation, and to divide an integer by 10N remove N zeros from its end — so long as it has them. Easy-peasy; my daughter knows all that.

Type
Articles
Copyright
© The Mathematical Association 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)