Roman numerals: Rules, Conversion, Sample Questions

Roman numeral is an ancient number system. The numbers are denoted as Roman alphabets. You must have noticed some clocks and your classes have the numbers written in a different number system than what we use usually, for example, class V, class VI. These are called Roman numerals. Roman numeral uses different alphabets to denote certain numbers, like five is denoted as V in the roman numeral, similarly, ten is denoted as X. In this article, we will learn more about roman numerals, the rules to write them, and the conversion process.

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Key takeaways: Roman numerals, Roman numeral chart, conversion, subtractive rule for roman numerals

What are Roman numerals?

Roman numeral is a number system that uses Roman alphabets to denote numbers. The alphabets used in Roman numerals are I, V, X, L, C, D, and M, denoting 1, 5, 10, 50, 100, 500, and 1000 in the Hindu-Arabic number system respectively. 

Roman numerals do not have a defined place for 0 (zero). It only represents fixed positive numbers. It was used in ancient times for day-to-day activities.

Roman numeral chart

Below is the chart for numbers 1 to 1000 in Roman numerals.

Roman numerals 1 to 100

As you see the below chart of Roman numbers from 1 to 100, you will be able to recognize a pattern. The basic numbers used in the Roman number system are I, V, X, L, C, D, and M. All the numbers are based on these few alphabets. For example, you can write anything after V by adding I to it, like VI, VII, VIII. And anything before X is written as IX rather than VIIII. These are some of the basic rules of writing Roman numbers. Below given is the chart from 1 to 100 in Roman numerals.

Rules to write Roman numerals

There are certain rules to write roman numbers. The rules are made to make it useful.

• If a lower digit is placed on the left side of the larger value digit, the lower value digit is subtracted from the larger value digit. For example, IX, as we already know I represents 1 and X represents 10, here I is lower in value than X, so IX represents 10-1 = 9
• Similarly, if a lower value digit is placed to the right of the larger value digit, it is added. For example, XII, here II is placed to the right side of X, so the number represented by XII is 10+2 = 12.
• Only the alphabets I, X, and C can be repeated. V, L, and D cannot be repeated.
• Any alphabet can be repeated only 3 times, not more than that. For example, to represent 30, you will write XXX, but for 40, you cannot write XXXX, rather the correct representation of 40 would be XL.
• When a bar over the alphabet is added, the number is multiplied by 1000. For example, X represents 10 x 1000 = 10,000.

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Conversion: Roman numeral to number

The rules for the conversion of Roman numerals to numbers are as follows:

• Rule 1: Add the value of symbols as many times as it is repeated if the higher value digit is placed to its left. 

Examples:

XVII = 10+5+1+1 = 17

XXXVI = 10+10+10+5+1 = 36

LVI = 50+5+1 = 56

• Rule 2: Subtract the value of symbols if a smaller value digit is placed before the higher value alphabet.

Examples: 

XL = 10-50 = 40

CM = 1000-100 = 900

XLIX = 50 - 10 + (10 - 1) = 49

Things to remember

• The number system that we use usually is the Hindu-Arabic number system. Apart from this, there is another number system called Roman numerals.
• Roman numerals are based on 7 basic numbers represented by Roman alphabets, namely, I, V, X, L, C, D, and M representing 1, 5, 10, 50, 100, 500, and 1000.
• When a lower value digit is placed to the right of the larger value digit, the lower value digit is added to the larger value digit. Similarly, when a larger value digit is placed to the right of the lower value digit, the lower value digit is subtracted.
• A bar is added over the alphabet to denote it is multiplied by 1000.
• Only the alphabets I, X, and C can be repeated. V, L, and D cannot be repeated. Each alphabet is repeated not more than 3 times.