Roman Numerals Explained: 8 Important Rules

In this blog, I'm going to show you the eight important rules you need to know in order to read Roman Numerals.

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Roman Numerals Explained: 8 Important Rules

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So today when we talk about numbers, the most common form is Arabic Numerals. That is one, two, three, and so on. 

However, if you take a look at some older prescriptions, you will not see Arabic numerals, but rather what you will see is Roman numerals.

Now, that is because in ancient times, Roman numerals were used for pharmaceutical computations and record keeping. So they were either used to specify the quantity of an ingredient in the apothecary system or to specify the units of dosage to be dispensed.

Now, in our current system of prescription writing, the use of Roman numerals is actually minimal.

However, they are used to represent the different schedules of controlled substances. So for example, scale to one, two, three, four, and five, and some physicians still use them in dosage calculations.

Therefore, as pharmacy students, pharmacy technicians, pharmacists, there's still a need to understand how to read Roman numerals.

Now, an Arabic number in the Roman system of numbers is designated by a letter.

Now, there are a stem of numbers that are used in the Roman system of numbers, and that is what is shown in the table. So you have 1/2 being "ss", 1 being "I", 5 being "V", 10 being "X", 50 being "L", 100 being "C", 500 being "D", and 1,000 being "M".

Now, these eight stem numbers serve as the building blocks by which other numbers in the Roman system are generated.

Now, in order to generate numbers in the Roman system, you need to understand and follow eight important rules.

Roman Numerals Rule #1: Rule of Addition

And the first rule is the rule of Addition. 

The rule of addition states that when a lower number is right after a higher number, you add all the numbers together.

Example 1

As an example, if you have XVI, the X is 10, the V is 5, and the I is 1. Now I is less than V, and the I is to the right of the V, and the V is to the right of the X. So X is 10, V is 5, and I is 1. So you add up the 10, the 5, and the 1, and you end up with 16.

Example 2

So let's look at another example. So here you have V, I, I, I, and so the I, which is 1, is to the right of V, and the I is lower than the V.

So you have V which is equal to 5, plus I which is equal to 1, plus I which is equal to 1, plus I, which is equal to 1. So 5 plus 1, plus 1, plus 1, and that gives you 8.

Roman Numerals Rule #2: Rule of Subtraction

Now, the next rule is the rule of Subtraction. 

So the rule of subtraction states that whenever a lower number precedes a higher number, the lower number is subtracted from the higher number.

Example 1

So as an example, you have IX, the I which is 1, precedes the X which is 10 and I is lower than X. So you have 10 minus 1 and that gives you 9.

Example 2

Another example, XL. X is 10, L is 50. The X precedes the L and X is lower than L. So you have 50 minus 10 and that would give you 40.

Now it's important to mention here that there are three numbers that are never to be subtracted from greater numbers and those numbers are V, D and L.

Roman Numerals Rule #3: Smaller Number Between Two Large Numbers

Now let's take a look at rule number three, which shows you what to do when you have a smaller number between two large numbers.

Example 1

Here we'll use an example to illustrate this rule. We have XIV, X equals 10, I equals 1, and V equals 5. Now I, which is 1, is smaller than X and V, so you have a smaller number between two large numbers.

Now because I precedes V, you will calculate it by taking five and subtracting one from that. That does based on rule number 2. That gives you 4. 

Now you have 4 which is to the right of a larger number, so you have 10 plus 4 and that gives you 14.

Example 2 

Let's take a look at another example. So here we have M, X and C, which is equal to 1090 in Arabic numbers. 

Now M equals 1,000, 10 equals 10 and C equals 100.

Now, 10 is smaller than 1,000 and smaller than 100. So you have the situation where you have a smaller number between two large numbers.

And so since the X precedes the C, we make use of rule number two, which is the rule of subtraction,

and you calculate it by having 100 minus 10, that gives you 90. Now 90 is to the right of a larger number, which is 1,000. So you add them using rule number one.

And so you have 1,000 plus 90, and that gives you 1090.

Roman Numerals Rule #4: Avoid the Repetition of More Than Three Consecutive Occurrences of the Same Letter

So the next rule, which is rule number 4, says to avoid the repetition of more than three consecutive occurrences of the same letter.

Example 1

So here we use an example to illustrate how this rule works. So if you have the number 8, which is the Arabic number 8, then it's given as VIII. So you have three "I"s after the V.

What you cannot do is say 8 = IIIIIIII, so eight “I"s.

That doesn't work because you are repeating the "I" more than three consecutive times.

 Example 2

Another example, 490 in Arabic numbers is going to be equal to CDXC

and not CCCCXC because you are repeating the C more than three consecutive times.

Roman Numerals Rule #5: Use the Largest Value Numeral

Rule number five, you need to use the largest value numeral. 

So in accordance with rule number four, when required, the largest value numeral should be used.

Example 1

So let's look at an example if we have the Arabic number 92, that should be equal to XCII

and not XXXXXXXXXXXII. So instead of using all those bunch of Xs,

we will rather use the larger value numeral, which would be C, and then put an X before that so that we can make use of the rule of subtraction, which is rule number two, and then add I, I to it, which would be using rule number one, the rule of addition.

Example 2

Let's look at another example. Arabic number 499 should be equal to CDXCIX 

and not CCCCXXXXXXXXXIX.

Here we are making use of rule number five by using the largest value number, which would be D in this particular example.

We have CD which gives us 400 instead of CCCC.

Then we have XC which gives us the 90 instead of nine Xs.

Then you add the IX which gives you the nine.

Roman Numerals Rule #6: The Power of 10

Rule number six, the power of 10. 

So the smaller number must be a power of 10 and cannot precede a number more than 10 times its value.

Example 1

So let's look at an example here 490 as an Arabic number and Roman numerals is going to be CDXC. So let's see how this works.

So the C which precedes the D, the C is a power of 10. That's 10 to the power 2. It's not more than 10 times the value of D. If you took C which is 100 and multiplied that by 10, that's basically 1,000, 1,000 is more than 500. So you can actually write CD.

Same thing for XC, X is a power of 10, X is 10, so that will be 10 to the power of 1. C equals 100. So 10 times X, will be 10 times 10, which is 100, and that's about the same value. So you can do CDXC.

Now, what you cannot do is XD. Even though X is still a power of 10, so 10 is equal to 10 to the power of 1. If you multiply 10 by 10 times its value, you get 100. But 100 is less than D, which is 500. So based on the rule of the power of 10, you cannot do that.

Example 2

Let's take a look at another example. So here you have 99 as an Arabic number, and that should be equal to XCIX as a Roman numeral.

Now the X which is 10, precedes C which is 100. X is a power of 10, which is 10 to the power of 1. And 10 times 10, will be 100, which is still equal to C. So you are good there.

Now I is still a power of 10, which is 10 to the power of zero. And if you multiply that by 10, you still have 10. So 10 is equal to X, which would be 10. And so you can still do XCIC.

What you cannot do is IC. And that is because even though I is a power of 10, basically 10 to the power of zero, if you multiplied I by 10 times its value, you get 10. And this 10 is less than C, which represents 100. So based on the rule of the power of 10, you cannot do that.

Roman Numerals Rule #7: Use Only One Preceding Smaller Number

Rule number 7, use only one preceding smaller number.

So there cannot be more than one smaller number in front of a larger number.

Example 1

Let's look at an example. So 48 in Arabic numbers will be equal to XLVIII.

What you cannot do is write the Arabic number 48 in Roman numerals as IIL. Because even though you may be trying to use a rule of subtraction, which is rule number two, you have more than one small number in front of a larger number. So that would violate rule number 7, and so you cannot do that.

Example 2

Let's look at another example. 97 as an Arabic number can be written as XCVII.

What you cannot do is write the Arabic number 97 as IIIC. Because you have more than one small number in front of a larger number. You have three I's in front of the C, so that violates rule number 7, and you cannot do that.

Roman Numerals Rule #8: Using a Bar 

Rule number 8, using a bar.

A bar placed on top of a letter increases the numerals value 1,000 times.

 Example 1

Let's look at an example. Here the Roman numeral XIX will be equal to the Arabic number 19.

But if you placed a bar on top of the XIX, now you have the Arabic number 19,000. And that is because the bar increases the numerals value 1,000 times.

Example 2

Let's look at another example. The Roman numeral VII is equal to the Arabic number 7.

But if you placed a bar on top of the VI, now you have the Arabic number 7,000. And that is because, once again, placing a bar on top of the Roman numeral increases its value 1,000 times. 

So I hope you found this tutorial useful. Thank you so much, and I will see you in the next blog.

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