# How to convert MMXVI? It is a valid Roman numeral. How to write it out as an Arabic number?

### 1. Roman numerals used to make the conversion:

#### I = 1; V = 5; X = 10; M = 1,000;

The numerals must be written from left to right in descending order; some symbols can be repeated up to 3 times in a row: I, X, C, M, (X), (C), (M).
Additive notation = a group of two or more numerals, equal or sorted in descending order from high to low - to calculate the value add up the symbols.
Additive notation of the Roman numerals

### 2. Add up all the values of the Roman numerals:

MMXVI =
M + M + X + V + I =
1,000 + 1,000 + 10 + 5 + 1 =
2,016

## Check the result (reverse the process). How to convert the Arabic number 2,016:

2,016 =
2,000 + 10 + 6;

### 2. Convert each subgroup:

2,000 = 1,000 + 1,000 = M + M = MM;
10 = X;
6 = 5 + 1 = V + I = VI;

2,016 =
2,000 + 10 + 6 =
MM + X + VI =
MMXVI;

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## The set of basic symbols of the Roman system of writing numerals

• ### (*) M = 1,000,000 or |M| = 1,000,000 (one million); see below why we prefer this notation: (M) = 1,000,000.

(*) These numbers were written with an overline (a bar above) or between two vertical lines. Instead, we prefer to write these larger numerals between brackets, ie: "(" and ")", because:

• 1) when compared to the overline - it is easier for the computer users to add brackets around a letter than to add the overline to it and
• 2) when compared to the vertical lines - it avoids any possible confusion between the vertical line "|" and the Roman numeral "I" (1).

(*) An overline (a bar over the symbol), two vertical lines or two brackets around the symbol indicate "1,000 times". See below...

Logic of the numerals written between brackets, ie: (L) = 50,000; the rule is that the initial numeral, in our case, L, was multiplied by 1,000: L = 50 => (L) = 50 × 1,000 = 50,000. Simple.

(*) At the beginning Romans did not use numbers larger than 3,999; as a result they had no symbols in their system for these larger numbers, they were added on later and for them various different notations were used, not necessarily the ones we've just seen above.

Thus, initially, the largest number that could be written using Roman numerals was:

• MMMCMXCIX = 3,999.