around 1900–1600 BCE
Babylonian Reciprocals Tablet
Old Babylonian reciprocal table (with errors)
Tablet YPM BC 024321 from the Yale University Babylonian Collection has been dated to around 1900–1600 BCE. Both sides contain two columns of numbers written in the base-60 numeral system of the Babylonians. The obverse (front) of the tablet consists of the whole numbers from 56 through 71 with their reciprocals. The reverse side similarly contains the numbers 72 through 80 with their reciprocals. In both cases, the numbers sometimes wrap around onto the sides of the tablet.
Babylonian reciprocal tables are relatively common, clearly demonstrating the ability of Babylonian scribes to perform simple arithmetic calculations. This tablet is notable for giving approximate base-60 values for the reciprocals it contains that cannot be expressed finitely in base 60. It is also noteworthy that the tablet contains a number of computational (or transcription) errors. For example, in the eighth line of the front of the tablet, the approximate reciprocal 1/63 ≈ 0.015873 should be given as 57, 8, 34 (equal to 57/60² + 8/60³ + 34/60^4 ≈ 0.015873) but is instead written as 57, 8, 24 (equal to 57/60² + 8/60³ + 24/60^4 ≈ 0.0158722).