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The Babylonian Numeration System

The Babylonian numeration system is based on powers of 60 (sexagesimal system). There are two symbols:

Small numbers are represented much like the Egyptian system. For example:

To represent larger numbers, use several groups of symbols, separated by spaces, and multiply the value of these groups by increasing powers of 60.

Q1.   Convert to Hindu-Arabic notation.

Because there is no symbol for zero, it is not always clear how many spaces are between symbol groups. For example:

The Babylonians used the symbol for subtraction.

For example, the numeral represents 20 – 3 = 17

To convert Hindu-Arabic numerals to Babylonian numerals, divide by powers of 60, similar to the way seconds are converted to hours and minutes.

Q2.   Write 12,221 as a Babylonian numeral.

Q3.   Write the Babylonian numeral as a Hindu-Arabic numeral.

Q4.   Write 745 as a Babylonian numeral.

Solutions:

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