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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: paseau@maths.ox.ac.uk

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

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