Expressing Roman Numerals to Hindu-Arabic System and vice-versa

The Roman Numeral System is an old numeration system that we still used today, you can find some on buildings, clocks and books. I will outline the approach I used in dealing with converting Roman numerals to Hindu-Arabic system and from Hindu-Arabic numerals to Roman numerals.

Before we begin, it is important that you are familiar with place values (e.g., ones, tens, hundreds etc.) , as this would be our key tool. Dealing with Roman Numerals, we need to familiarize ourselves with some ground rules.

I. Get familiar with the basic Roman Numerals with fixed values.

 Hindu-Arabic Numerals 1 5 10 50 100 500 1000 Roman Numerals I V X L C D M

II. We add the Hindu-Arabic values for same or smaller values that is written on the right side of a Roman numeral.

Example:  XXII = 10+10+1+1 = 22

III. We subtract the Hindu-Arabic values for smaller values that is written on the left side of a Roman numeral.

Example: XL = 50 – 10 = 40

IV. Roman numeral symbols I, X, C and M can be written three times in a sequence.

Example: CCC = 100+100+100 = 300

V. Roman numeral symbols V, L, and D cannot be written repeatedly in a sequence.

It would be helpful if you get familiar with the table below:

 Hindu-Arabic Numerals 4 9 40 90 400 900 Roman Numerals IV IX XL XC CD CM

Identifying the Place Values plays a key role in expressing Roman numerals to Hindu-Arabic and from Hindu-Arabic to Roman Numerals.

Expressing Roman Numerals to Hindu-Arabic Numerals. Our approach is laid out in the following steps

Take for example: CCXXIX

1. Identify the place values involved. Looking at our example the presence of the Roman numerals C indicate that we are dealing with a 3-digit Hindu-Arabic numeral to it’s hundreds place.

2. Group the Roman numerals according to their place values.

 Hundreds Tens Ones CC XX IX

3. Get the respective Hindu-Arabic values in each place values. (Use the ground rules (II and/or III), we laid out earlier on this article, as necessary)

 Hundreds Tens Ones CC XX IX 100+100 10+10 10-1

4. Get the sum of the resulting numbers in each place values.

 Hundreds Tens Ones CC XX IX 200 20 9 229

More examples:

Example: XCIV

 Hundreds Tens Ones XC IV 100-10 5-1 90 0 4 94

Example: DXV

 Hundreds Tens Ones D X V 500 10 5 515

Expressing Hindu-Arabic Numerals. Our approach is basically the same as mention above but this time it’s the other way around

Take for example: 612

1. Identify the place value involved. We can clearly see that this one contains a hundreds place value

2. Expand the Hindu-Arabic numeral according to its place values.

 Hundreds Tens Ones 600 10 2

3. Convert each Hindu-Arabic place values to Roman symbols. Use the ground rules as necessary.

 Hundreds Tens Ones 600 10 2 DC X II

4. Combine the resulting roman numeral symbols in each place value, starting from left to right.

 Hundreds Tens Ones 600 10 2 DC X II DCXII

More examples:

Example: 974

 Hundreds Tens Ones 900 70 4 CM LXX IV CMLXXIV

Example: 450

 Hundreds Tens Ones 400 50 0 CD L CDL