** Roman Numerals and Roman Numbers **

Roman numerals were invented as the Romans needed a system to 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. The Romans adopted the numeral system from their predecessors in central Italy, the Etruscans, they simply adapted and improved the system.

** Roman Numerals Chart **

** An Introduction to Numerals **

Roman numerals are represented by seven different letters: I, V, X, L, C, D and M , which represent 1, 5, 10, 50, 100, 500 and 1,000. We use these seven letters to make thousands of different numbers. The Roman numeral two for example; looks like II , which is just two one's combined together. The numeral twelve is written as; XII , which when broken down is 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 , which all together comes to twenty-seven.

Roman numerals are usually written largest to smallest from left to right, this tell us that we must add the numerals together. However, this is not always the case. The Romans didn't like four of the same numerals to be written in a row, so they developed a system of subtraction. For example; the number four is usually written as IV, because the smaller I or 1 is before the larger V or 5 we subtract one from five, which gives us four. The same principle applies to the number nine which is written as IX, because the smaller I or 1 is before the bigger X or 10 we subtract one from ten which gives us nine. There are six instances where the Romans used subtraction.

⋅ 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 1904 is a great example of the above rules. The number 1904 is represented by the Roman numerals MCMIV. If we break it down then; M = 1,000, CM = 900 and IV = 4. Use the Roman numeral converter above to find more examples of these rules!

** Years and Dates **

Roman numerals are sometimes used to represent the year. In order to write the year we need to know how to write large numerals, which can be tricky. We will look at a few examples and break them down to work out the year.

To start with let's look at an easy one, the year 2000 for example is simply MM (1000+1000). However, we have to be careful with years from the 20th century as there is an element of subtraction. 1900 is written as MCM, and because the smaller C or 100 is before the second M or 1000, we must subtract 100 from 1000 which is equal to 900. So 1950 for example is MCML (1000 + 900 + 50). Years in the 21st century are a little easier. First we start off with the 2000 (MM) and then add the appropriate number. For example; 2015, to write this we start off with MM or 2000 and then add on 15 which is XV, all together it looks like MMXV.

** Large Roman Numerals **

Because numerals only use seven different letters, with the largest of those letters representing 1000, it makes it difficult to write very large numbers with numerals. In fact, the Romans rarely needed to write numbers larger than 3,999 so never developed a system to do so. It wasn't until much later that a system was developed in order to do so.

In this system, you draw a line across the top of the numeral to multiply the numeral by 1,000. As seen in the image to the right, 5,000 is written as (5 x 1000). Similarly, 1,000,000 is written as (1000 x 1000).

So if we wanted to show 1,550,000 in Roman numerals it would look like: , if we break it down then = 1,000,000, = 500,000 and = 50,000. Use the Roman numeral converter at the top of the page to look for more examples.

** 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 with Numerals **

Because there is no numeral for zero it makes advanced mathematics a little more difficult. The Romans probably didn't use numerals to complete arithmetic due to its complexity, for example; multiplication and division are far too impractical. However, it is not impossible to use numerals to complete addition and subtraction.

### Addition

Before we start, it is important to note than when adding with Roman numerals that we don't use the subtractive principle. For example; the number four is not shown as IV but as IIII. We will see why in a second. So let's start with a simple problem; in order to add IX and XI together, we must first change the nine (IX) to VIIII, because it uses the subtractive principle. So now we are left with VIIII + XI. After ensuring there are no numerals which use the subtractive principle we may continue with the problem. As we can see in the image we can complete the sum just like we would if we were using Arabic numbers. We arrange the numerals in order from biggest to smallest, which gives us XVIIIII. The next step is to simplify the IIIII into V, which gives us XVV, which can then be further simplified to XX or 20. Simple!### Subtraction

Just the same as addition we don't use the subtractive principle when doing sums which involve subtraction. So let's try one, we're going to try and subtract CCLXXXVIII from CCLXXII. The first step is to write the sum out, as seen in 'Step 1', secondly we cross out pairs of numerals as seen in 'Step 2', which gives us a much easier sum to deal with: XVIII - I, which is equal to XVII or 17.** Modern Uses of Roman Numerals **

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 was the eighth king of England to be called Henry, by using numerals we can easily distinguish between which King Henry we are talking about! |

II. |
Many competitions such as the Olympic Games and the Super Bowl use numerals to signify how many times the event has preceded the current one. For example; the Olympic Games in Brazil in 2016 will be the 31st Games, so it will the XXXI Games. |

III. |
Numerals can often be found on buildings and monuments to illustrate the year of construction. For example; a building that was built in the year 2004 may have the numerals MMIV engraved upon it. |

IV. |
Many movies use Roman numerals to illustrate in which year the film was copyrighted or created. For example; the movie 'Gladiator' was copyrighted in the year 2000 so it may have the numeral MM at the end of the credits. Or the film 'Spartacus' which was copyrighted in the year 1960 so will have the numeral MCMLX. |

V. |
A lot of clocks use numerals to represent the hours. For example; 6 o'clock is VI and 10 o'clock is X. |

Numerals can be found in so many real life situations. The list goes on and on; at the beginning of books to number the pages before the novel begins, within legislation to label sections, sub-sections etc. and even to refer to wars; such as, WWI and 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!