Rules for the construction of Roman numerals

Source: Internet
Author: User

Roman Numerals

Roman numerals are the counting system of the Roman period, and the earliest digital representations, mostly for clocks, calendars and chapter numbering. It is generally believed that Roman numerals are used only for counting and not for calculation. Like II,IV,VII, these are common Roman numerals.

Constructing rules

Roman numerals can represent all positive integers by repeating or combining 7 different letters (no 0 in Roman numerals).

    • I = 1
    • V = 5
    • X = 10
    • L = 50
    • C = 100
    • D = 500
    • M = 1000

1, the letter can be superimposed.

If I means 1,ii means that 2,III represents 3. VI means 6 (V=5,i=1,vi is v+i, equals 6), and VII means that 7,VIII represents 8.

2, the letter expressed as a multiple of 5 (V,L,D) shall not be repeated. The remaining letters (I,X,C,M) can be repeated up to 3 times.

(1) If 10 should be represented as X, not vv. Again, it should be expressed as XV, not VVV.

(2) If 4 can not be represented as IIII, but should use the next largest with five characters to reduce the operation is obtained, expressed as IV (according to Rule 3, the high of I is 1, the low of V is 5, the high is less than the low, so lower the high position with low, 5-1=4). Similarly, 9 cannot be expressed as XIIII, because I repeats 4 times. and to represent it in the form of 10-1, IX.

3. Roman numerals are generally written from high to low and read from left to right. If the number in the high position is larger, the number of high-level plus the low number, and if the number at the high position is smaller, the number of the high is subtracted from the low number.

such as CDs and DC represent 400 and 600, respectively. CD, C in the high, it represents the number is 100,d in the low, it represents the number is 500, the high number is less than the low number, so the low D (500) minus the high of C (100), the CD represents 400, and in the DC, d in the high, the number is 500,c in the low, the number is 100 , the high number is higher than the low number, so the high level plus low, 500+100, the DC is 600.

4, low-level minus the high can not cross one digit and the number of high can only be i,x,c (that is, only minus 1, minus 10, minus 100).

(1) If 99 cannot be expressed as 100-1, namely IC. Because C represents 100 and I represent more than one digit between 1. 99 should be expressed as (100-10) + (10-1), i.e. XCIX.

(2) If 45 can not be expressed as 50-5, because 50-5 is to be written as VL, and the lower position minus the high, the number of high can only be i,x,c, obviously not. So 45 can only be written as (50-10) + 5 in the form of XLV.

5. Add a horizontal line or a subscript to the Roman numerals to multiply the number by 1000. Similarly, the two horizontal lines are multiplied by 1000000.

As long as you understand the above 5 rules, you can convert between Roman numerals and Arabic numerals in any way. Finally, a Roman numeral table is attached:

Rules for the construction of Roman numerals

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