The opposite conversion - from decimal to octal - is accomplished by an elegant method in which the remainders from division operations and the integral parts of products play leading roles.

You recall that before you knew about decimal fractions, when you had to work a division problem that did not “come out even.” you simply noted the remainder instead of carrying the quotient out to a decimal fraction. For example, 25 divided by 8 results in a quotient of 3, with a remainder of 1. (The following calculations are all done with decimal numbers.)