Why is the letter L the roman numeral for 50?

Answer 1

The origin of the letters is not known with any certainty. One theory is that they derive from tally stick notches. The counter would score a notch in the stick for each item they were counting. The fifth notch would gain an extra stroke, creating a type of V shape. The tenth notch was crossed through creating an X shape. The fifteenth notch would be a V, the twentieth an X, and so on, until the 49th notch. The next notch (the 50th) is thought to have originally been an inverted T, which later became symbolised by the letter L.

The theory has some credence due to the way the tally can be reduced to the standard notation we are familiar with today.

If the tally were, say, 56, the following series of notches would be created:

IIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIILIIIIVI

When the scribe came to record the tally, they would reduce it using a simple shorthand. Reading from the right, locate the largest value. In this case we find an L, with nothing equal or larger before it. Thus everything preceding that L can be ignored (they are implied). Thus the notation is reduced to:

LIIIIVI

We then repeat the process using the next highest value, which in this case is V. The presence of a V implies that 4 'I's must precede it, so they can also be ignored, leaving us with:

LVI

Thus we have the Roman numeral for 56.

The convention of using subtractive notation such as IV instead of IIII, and IX instead of VIIII, is thought to have been introduced much later. Sometimes you will encounter both notations in the same sequence. For instance, clock faces that use Roman numerals usually represent 4 with IIII and 9 with IX, as it is more aesthetically pleasing (both symmetrically and radially). However, modern conventions that have been in use for a few hundred years state that no numeral may be repeated more than three times in succession. Thus 3999 is the largest number that can be represented by Roman numerals (MMMCMXCIX).