Decimal Fractions

The history of the theory of decimal fractions is an interesting elementary study. The following paper discusses how to convert repeating decimals into fractions. But there is much more to the theory than this. For example, if you have a fraction, how many places will there be in its repeating decimal?

A mathematician that contributed to the theory of repeating fractions was John Wallis. Look at what he said in his Treatise on Algebra (1885).

Robinson, John, "On the theory of circulating decimal fractions," Philosophical Transactions of the Royal Society of London, vol. 58 (1768), pp. 207-213. This is readily available in a 1965 Johnson reprint. One line in this paper that especially pleased me was this: "The circulating fraction of 0,999, &c. is equal to 1, 0." Was this known before 1786?

Return to the minicourse home page.
If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu
Posted 2 December 1996. Revised 20 January 1997 and 4 January 2003.