## Overview

Roman numerals were developed so that the Romans could easily price different goods and services. Roman numbers were widely used throughout the Roman Empire in everyday life. Following the fall of the Roman Empire, numerals continued to be used throughout Europe up until the 1600's.

## Introduction

Roman numerals are represented by seven different letters: I, V, X, L, C, D and M. Which represent the numbers 1, 5, 10, 50, 100, 500 and 1,000. These seven letters are used to make thousands of numbers. For example, the Roman numeral for two is written as 'II', just two one's added together. The numeral twelve is written as, XII, which is simply X + II. If we take this a step further; the number twenty-seven is written as XXVII, which when broken down looks like XX + V + II.

Roman numerals are usually written largest to smallest from left to right. However, this is not always the case. The Romans didn’t like four of the same numerals written in a row, so they developed a system of subtraction.

The Roman numeral for three is written as ‘III’, however, the numeral for four is not ‘IIII’. Instead we use the subtractive principle. The number four is written as ‘IV’, the numerals for one and five. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as ‘IX’. There are six instances where subtraction is used:

⋅ I can be placed before V (5) and X (10) to make 4 and 9.
⋅ X can be placed before L (50) and C (100) to make 40 and 90.
⋅ C can be placed before D (500) and M (1000) to make 400 and 900.

The number 1994 is a great example of these rules. It is represented by the Roman numerals MCMXCIV. If we break it down then; M = 1,000, CM = 900, XC = 90 and IV = 4.

#### Example: 16

In order to make the number 16 we must take the numerals for 10 (X), 5 (V) and 1 (I), thus making XVI.

#### Example: 27

In order to make the number 27 we must take the numerals for 20 (XX), 5 (V) and 2 (II), thus making XXVII.

#### Example: 32

In order to make the number 32 we must take the numerals for 30 (XXX) and 2 (II), thus making XXXII.

#### Example: 58

In order to make the number 58 we must take the numerals for 50 (L), 5 (V) and 3 (III), thus making LVIII.

#### Example: 183

In order to make the number 183 we must take the numerals for 100 (C), 50 (L), 30 (XXX) and 3 (III), thus making CLXXXIII.

#### Example: 555

In order to make the number 555 we must take the numerals for 500 (D), 50 (L) and 5 (V), thus making DLV.

#### Example: 1582

In order to make the number 1582 we must take the numerals for 1000 (M), 500 (D), 50 (L), 30 (XXX) and 2 (II), thus making MDLXXXII. ## Years and Dates

To write the year in Roman numerals we need to make larger numbers. Let’s look at a few examples.

Years in the 21st century are quite simple. First, we start off with MM (1000 + 1000) and then we add on the appropriate amount. So, if we want 2020 in numerals we start with MM (2000) and add XX (20) to make MMXX.

Years from the 20th century are simple as well. We start off with the Roman numerals for 1900 (MCM) and add on the appropriate amount from here. So, for example, 1985 would be written as MCM (1900) + LXXX (80) + V (5) = MCMLXXXV. ## Large Roman Numerals

Because the largest letter used is M and we can only stack three of the same numeral together the largest number you can make in Roman numerals is 3999 (MMMCMXCIX).

However, it is possible to write numbers higher that 3999 in Roman numerals. In this system, you draw a line across the top of the numeral to multiply it by 1000.

For example, the Roman numeral for 5000 (5 x 1000) is written as: . Similarly, 1,000,000 (1000 x 1000) is written as .

If we want to write 1,550,000 in Roman numerals it would look like this: . If we break it down the numeral for 1,000,000 is , the numeral for 500,000 is and the numeral for 50,000 is . ## Zero and Fractions

Fractions were often used in currency. The most common fractions used were twelfths and halves. A twelfth is represented by a single dot '•', which is known as an 'uncia'. A half is represented by the Latin letter 'S', which is short for semis.

This isn't really a rule, but interestingly, there is no numeral to represent zero. This is because the system of Roman numbers was developed as a means of trading and there was no need for a numeral to represent zero. Instead they would have used the Latin word 'nulla' which means zero. ## Adding and Subtracting

As there is no Roman numeral for zero it makes advanced mathematics quite difficult. It is possible to easily use numerals for addition and subtraction. However, multiplication and division are far too impractical.

#### Addition

When we are adding with numerals it is important that we ignore the subtractive principle. For example, the number four is written as IIII rather than IV.

Let’s use a simple example: to add IX and XI we must first change the IX in to VIIII. Next, we arrange the numerals in order from biggest to smallest, which gives us XVIIIII. The next step is to simplify the IIIII to V which gives us XVV, which can be further simplified to XX or 20. Simple! #### Subtraction

When we subtract numerals we also ignore the subtractive principle. Here’s the sum: CCLXXXVIII - CCLXXII. The first step is to write it out, as seen in the image below. Secondly, we scratch out all the pairs of numerals. This leaves us with a very simple sum to calculate: XVIIII which is equal to XVII or 17. ## Modern Uses of Roman Numerals

Roman numerals can still be seen in the modern day, in fact they are all over the place!

 I. Roman numerals are used to refer to kings, queens, emperors and popes. For example; Henry VIII of England and Louis XVI of France. II. Many competitions such as the Olympic Games and the Super Bowl use numerals to represent how many times the event has been held. For example, the Olympic games in Tokyo (2020) will be the thirty-second time the event will be held and will be represented by the numerals XXXII. III. Numerals can often be found on buildings and monuments to signify the year of construction. For example, a building built in 2004 may have the numerals MMIV engraved on it. IV. Many movies use numerals to illustrate the year the film was made. For example, 'Gladiator' was copyrighted in the year 2000 so it has the numerals MM at the end of its credits. Another example is the film 'Spartacus' which was copyrighted in 1960 and has MCMLX at the end of its credits. V. Many clocks also use numerals to represent the hours.

Roman numerals can be found in many other places; the list goes on and on. It is used at the start of books to number pages, to label sections and sub-sections in legislation and contracts, to reference wars (WWI & WWII).

## Origin of Roman Numerals

There were a number of counting systems in the ancient world prior to the creation of Roman numbers. For example, the Etruscans, who lived in central Italy before the Romans, developed their own numeral system with different symbols.

#### Theory 1

A common suggested theory for the origin of the Roman numbers system is that the numerals represent hand signals. The numbers; one, two, three and four are signalled by the equivalent amount of fingers. The number five is represented by the thumb and fingers separated, making a 'V' shape. The numbers; six, seven, eight and nine are represented by one hand signalling a five and the other representing the number 1 through to 4. The number ten is represented by either crossing the thumbs or hands, signalling an 'X' shape.

#### Theory 2

The second theory suggests that Roman numerals originate from notches which would be etched onto tally sticks. Tally sticks had been used for hundreds of years previous to the Romans and were still used up until the 19th century by shepherds across Europe.

The numbers one, two, three and four were represented by the equivalent amount of vertical lines. The number five represented by an upside down 'V'. The number was represented by an 'X'. In order to make larger numbers they would use the same rules as numerals did.

For example; seven on a tally stick would look like: IIIIVII, when shortened it would look like VII, identical to Roman numbers. Just like the above example the number seventeen, in long form, would look like IIIIVIIIIXIIIIVII, however, this in short form would look like XVII, which is also identical to numerals.

Certain Roman numerals; for example, four when written on a tally stick would like this: IIIIV. When the tally was re-written at a later date four could be written as either IIII or IV. As the Roman number system was developed further it adapted the number 50 to be represented by the letter 'L'. Similarly, the number 100 was illustrated by a wide array of symbols, most commonly, represented by the numeral 'I' on top of an 'X'.

The numbers 500 and 1000 were represented by a 'V' and 'X' in a circle respectively. As the Roman Empire grew these symbols were replaced with a 'D' (500) and 'M' (1000). The Latin letter M was short for 'mile', which is translated as one-thousand.

## Other Number and Counting Systems

Prior to Romans numerals there were many civilisations who had invented and used their own counting and number systems. We are going to take a quick look at Egyptian, Babylonian and Arabic number mechanisms.

#### Egyptian numbers: 3000-1600BC

One of the oldest number systems we have comes from ancient Egypt, with the earliest record being recovered from 3000BC, over 5000 years ago. The Egyptian counting system was very comprehensive compared to others, they even had a symbol to represent infinity!

In this system the number 1 was represented by a straight line, just like Roman numerals. The number 10 is represented by a semi-coiled length of rope and 100 being represented by a coiled rope. As the numbers get larger they are represented by other symbols. The number 1,000 is illustrated using a water lily or lotus. The symbol for 10,000 is a large upward facing finger. The figure 10,000 is represented by a frog and finally 1,000,000 is represented the Egyptian god Heh.

The Egyptians unlike the Romans didn't use the subtraction rule, instead they would just use the symbols for 1, 10, 100, 1,000 and so on. For example; the number 3 is illustrated by 'III', similarly the number 9 is represented by 'IIIIIIIII'. #### Babylonian numbers: 1750BC

The Babylonian number system was one of the more complicated arithmetic systems. The Babylonian civilisation adopted the system from another much older civilisation, the Sumerians. Similar to Roman numerals there is no figure to represent zero. Another major flaw in this system is that the symbol for both one and sixty are the same!

Similar to the Egyptian numeral system 1 to 9 would be represented by the equivalent amount of single units. For example; the number 3 is written as . This is the same for multiples of 10 and thus the number 20 is written as . Using these examples we can make the number 23, which is written as  .

Similar to Roman numerals there is no figure to represent zero. As we use one to ten as our base, the Babylonians would use one to sixty, furthermore the symbols for one and sixty were the same! 