Changing Representations

You may wish to change the representation of a number from base 5 notation into base 10 notation. Do this by symbol replacement. Change the base 5 symbols into the base 10 symbol equivalents. Then do the arithmetic in base 10.

4215	=	4 × five2 + 2 × five1 + 1 × five0
the number in base 10	=	4 × 52 + 2 × 51 + 1 × 50
the number in base 10	=	4 × 25 + 2 × 5 + 1 × 1
the number in base 10	=	100 + 10 + 1 = 111

The above process is often called "converting a number from base 5 to base 10". But in fact, the number is not being converted, its representation is being converted. The characters "421 (base five)" and "111 (base ten)" represent the same number.