By: Tao Steven Zheng (郑涛)

【Problem】

The ancient Babylonians adopted a sexagesimal (base 60) place-value system for calculation. For example, the number   in base 60 is equal to the number 7397 in base 10.

Here, the commas separate the digits of each place value  etc. Another example, the number  in base 60 is equal to the number 62.1175 in base 10.

Here, the semicolon acts like a decimal point and the following commas separate the digits of each place value etc.

The ancient Babylonians also invented the concept of zero long before the ancient Indians; however, the Babylonian zero served as a placeholder for writing numbers where certain place-values are not a number between 1 and 59.

Problem 1: Convert the number  to base 10.

Problem 2: Convert the number to base 10.

Problem 3: Convert the number to base 10.

【Solution】

Problem 1

Problem 2