# 4 Disadvantages of Roman Numerals

Originated in ancient Rome, Roman numerals were the common way of expressing numbers in Europe throughout centuries. Their use continued long after the fall of the Roman Empire into the Middle Ages. However, starting with the 14th century, Roman numerals were gradually replaced by Hindu-Arabic numerals. Although this change encountered some resistance at the time, it became accepted in time that the Arabic numerals had many practical advantages over the Roman numerals. So what were the disadvantages of Roman numerals? Why don’t we use Roman numerals today?

#### Lack of Zero

In a modern world dependent on Arabic numerals, one might find it surprising that the Roman numeral system did not have a symbol to represent the number zero (0). The Roman numerals consist of seven symbols used to express all the other numbers and there is actually no letter for zero. However, this does not mean that the Romans were not familiar with the concept of ‘nothingness’. Instead of assigning a specific symbol, the Romans used nulla, the Latin word meaning ‘none’, whenever they needed to express zero or ‘nothingness’.

Actually, the lack of zero was not a big problem for the Romans at the time because they were able to convey ‘nothingness’ on their counting boards (abacus) by using empty spaces. Not having a symbol for zero was possible also because the Roman numeral system is not positional as the Hindu-Arabic system. Although Roman numerals are a de-facto ‘base ten’ numbering system, they are not expressed with place value notation. Therefore, this system did not need a specific ‘digit’ for zero to convey it. However, it is now obvious that the presence of 0 makes life easier and practical in terms of notation, everyday life and scientific purposes. Therefore, looking from today’s perspective, lack of zero is one of the main disadvantages of the Roman numeral system.

#### Hard to Calculate

Try solving the following equation without using or even thinking about Arabic numbers: CCLXX + DCCCLXXXVIII. Then consider 280 + 888. The Roman numerals make it hard to add, subtract or multiply numbers, let alone division. Yes, the use of abacus made it easier to do operations with Roman numerals but it wasn’t practical for the common people to manage everyday calculations or simple accounting with Roman numerals. On the other hand, the adoption of Hindu-Arabic numerals enabled even the illiterate to understand and write numbers. Most importantly, it paved the way to advances in mathematics and other scientific interest areas in the Western world.

#### Fractions

Another disadvantage of the Roman numerals is the somewhat complicated way of writing fractions. For expressing fractions, the Romans used a base 12 system, namely a duodecimal system. They also named the fractions with words. The base 1⁄12 was named ‘uncia’ (later to be known as ounce) and represented with a single dot. Dots were added one by one to represent the fractions until 1⁄2, which was signified with a capital S (for semis, meaning half). After this point, dots were placed next to S until I (1) was reached.

Building on uncia (1⁄12 ), they used the fractions with the following names:

• 1⁄12: Uncia, represented with ·
• 2⁄12 = Sextans, represented with ·· or :
• 3⁄12 = 1⁄4: Quadrans, represented with ··· or ∴
• 4⁄12 = 1⁄3: Triens, represented with ···· or ∷
• 5⁄12: Quincunx (five ounce), represented with ····· or ⁙
• 6⁄12 = 1⁄2: Semis (half), represented with S
• 7⁄12: Septunx (seven ounce), represented with S·
• 8⁄12 = 2⁄3: Bess, represented with S·· or S:
• 9⁄12 = 3⁄4: Dodrans, represented with S··· or S∴
• 10⁄12 = 5⁄6: Dextans, represented with S···· or S∷
• 11⁄12: Deunx, represented with S····· or S⁙
• 12⁄12 = As, represented with the numeral I

Using a base 12 system rather than a base 10 system enabled the Romans to handle fractions like 1⁄3 and 1⁄4 easier and faster. However, the overall notation for expressing fractions was hard in comparison to the Hindu-Arabic system. In addition, it is not quite possible to express precise numbers that are not fractions of 12.

#### Not Easy for the Common People

Understanding the Roman numeral system required at least basic knowledge of specific rules. For example, writing even the basic number 174 (CLXXIV) would require a person to know not only the values of the symbols but also how to do addition and subtraction. As mentioned above, this way of expressing numbers meant that not everybody in a society could understand the numbers, let alone do any calculations, trade and accounting. Therefore, it is not a coincidence that in the 14th century, the merchant class was quite willing to adopt the Hindu-Arabic numerals for accounting.