Why are MAC addresses written as six pair of Hexadecimal numbers?

Answer 1

Any data is stored internally in the computer as binary digits, but those are "bulky" - you need 4 binary digits for every hexadecimal digit, so hexadecimal is really a kind of shortcut to write out binary numbers.

Decimal is another option, but conversion between binary and decimal is more cumbersome than with hexadecimal. Therefore, for the new IP addresses (IP version 6), they decided to write them down in hexadecimal, instead of the decimal that is used for IPv4.