Below is the base 60 system used by Babylonians? Using the the translation table translate the following: #B->Decimal# a) 2, 25 b) 3, 36; 22, 32, 45 #Decimal->B# a) 1245 b) 65 c) 147 Compare to decimal and give some comments?

Hence Babylonian system can lead to multiple values when converted to decimal or any other base system.

If above constraints are ignored and one focuses primary on the question, the following are the decimal values of given Babylonian numbers

To translate from the base 60 system used by the Babylonians to decimal:

a) For 2, 25: [ 2 \times 60 + 25 = 145 ]

b) For 3, 36; 22, 32, 45: [ 3 \times 60^2 + 36 \times 60 + 22 \times 60^0 + 32 \times 60^{-1} + 45 \times 60^{-2} ] [ = 10800 + 2160 + 22 + \frac{32}{60} + \frac{45}{3600} ] [ = 12982.75833333 ]

To translate from decimal to the base 60 system used by the Babylonians:

a) For 1245: [ \frac{1245}{60^0} = 1245 ]

b) For 65: [ 65 \div 60 = 1 \text{ remainder } 5 ]

c) For 147: [ 147 \div 60 = 2 \text{ remainder } 27 ]

Comparing to decimal:

For the first set:

a) 2, 25 in base 60 translates to 145 in decimal.

b) 3, 36; 22, 32, 45 in base 60 translates to approximately 12982.75833333 in decimal.

For the second set:

a) 1245 in decimal translates to 1245 in base 60.

b) 65 in decimal translates to 1, 5 in base 60.

c) 147 in decimal translates to 2, 27 in base 60.

The Babylonian base 60 system allows for a compact representation of large numbers due to its positional notation. However, arithmetic operations might be more complex compared to the base 10 system commonly used today.