The Babylonians used a system similar to our decimal system to express fractions, except they used base 60, so they would have a “sixtieths” place instead of a “tenths” place. This is called a sexigesimal system. For example, .(30) in their system (which would be written using their numerals, not Hindu-Arabic) would mean “thirty sixtieths” and would correspond to .5 in our system (“five tenths”).

(a) Write 3/10 as a decimal and as a sexigesimal.

(b) Are there any fractions that can be written as a finite sexigesimal, but not as a finite decimal? If so, give an example.

(c) In some Babylonian texts, there are sentences such as “seven does not have an inverse.” What do you think they meant by this?