In Roman numerals, the number 4 is written as IV and 6 is written as VI due to the subtractive and additive principles of the numeral system. The Roman numeral system uses letters to represent numbers: I for 1, V for 5, X for 10, L for 50, C for 100, D for 500, and M for 1000. When a smaller numeral appears before a larger numeral, it is subtracted from the larger numeral. This is why 4 is written as IV (5 – 1 = 4). Conversely, when a smaller numeral appears after a larger numeral, it is added to the larger numeral. This is why 6 is written as VI (5 + 1 = 6). This system allows for efficient representation of numbers using a combination of letters and avoids the need for additional symbols.