| Week | Topic and action |
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| Week 35 | |
Roman Numerals
- Roman numerals are a numeral system of ancient Rome based on letters of the alphabet, which are combined to signify the sum (or in some cases, the difference) of their values.
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| Symbol | I | V | X | L | C | D | M |
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| Value | 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
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- The first ten Roman numerals are: I, II, III, IV, V, VI, VII, VIII, IX, X. The table below also list Roman numerals of tens, hundreds and thousands (up to 3000).
| I(1) | II(2) | III(3) | IV(4) | V(5) | VI(6) | VII(7) | VIII(8) | IX(9) |
| X(10) | XX(20) | XXX(30) | XL(40) | L(50) | LX(60) | LXX(70) | LXXX(80) | XC(90) |
| C(100) | CC(200) | CCC(300) | CD(400) | D(500) | DC(600) | DCC(700) | DCCC(800) | CM(900) |
| M(1000) | MM(2000) | MMM(3000) | | | | | | |
- Additive principle: If the symbols are arranged from left to right in descending based on their values, the value of the Roman number is the sum of all of the numerals:For example,
II = 1 + 1 = 2, VII = 5 + 1 + 1 = 7, XVIII = 10 + 5 + 1 + 1 + 1 = 18.
- Subtractive principle: if a symbol of smaller value precedes a symbol of larger value, the smaller value is subtracted from the larger value, and the result is added to the total.
For example, IV = 5 − 1 = 4, IX = 10 − 1 = 9, XIX = 10 + (10 − 1) = 19, CMXLIV = (1000 − 100) + (50 − 10) + (5 − 1) = 944.
The Rules to form a Roman numeral
- The letters should be arranged from the one with the largest value to the one with the smallest. Each letter's value is added to the previous ones.
- Only powers of ten (I, X, C, M) can be repeated. Do not repeat any letter more than three times in a row. For example, 10 is X not VV, and 4 is IV not IIII.
- Because of the preceding rule, certain numbers must be written using subtraction. In this case, a letter with a smaller value precedes one with a larger value and the value of the smaller is subtracted from the larger. The result is then added to the rest of the letters. The following rules apply to subtraction:
- Only powers of ten (I, X, C, M) can be subtracted. For example, 45 is XLV not VL, 15 is XV not XVX.
- The smaller letter must be or of the larger one. For example, 99 is XCIX not IC (since I is not or of C).
- The smaller letter must be either the first letter or preceded by a letter at least ten times greater than it.
- If another letter follows the larger one, it must be smaller than the number preceding the larger one. For example, 140 is CXL not XCL because L (50) isn't smaller than X (10)
- To put it most concisely: When converting to Roman numerals, convert each digit separately. For example,
- for 863 convert 800, 60, and 3 to give DCCC, LX, and III to get DCCCLXIII.
- for 386 convert 300, 80, and 6 to give CCC, LXXX, and VI to get CCCLXXXVI.