Roman Numerals

What do you understand by numerals? Numerals represent a numeric quantity. Is there any other way to write the numerals other than the most commonly used way of writing numbers? Yes, you can. You can use counters to represent your numbers. Further, you can even use tally marks for the same.

Roman letters table
Roman Letters Table

If you dig the history, you will come across that Romans in ancient times used different representations for conveying the idea of numbers. They used the English alphabet as a symbol to represent the numbers. This method of representing numbers is widely known as Roman Numerals. Thus, it is an ancient method of representing numbers.

Roman Numerals Symbols
Roman Symbols

How can you write numbers in Roman numerals?

To represent the numbers in Roman numerals you have to follow certain rules and regulations. You will observe the conversions involve a set of fixed rules. The numbers can be converted to Roman numerals and vice-versa.

It’s time to do brainstorming!

The clocks or wristwatches use Roman numbers from 1 to 12. The clock uses Roman numbers like I, V. X, etc. And, the basic knowledge about Roman numbers helps to read the time in these clocks. Presently, Roman numbers have limited use.

Thus, some of its usages can be seen in the wall clock, book chapter headings, film titles, designating the level of class, suffixes in the family generation of Kings and other prominent personalities, etc.

Roman Numerals

As the name suggests Roman numbers have their roots in Rome, in ancient times. Romans used these in their daily life transactions. And, they found it easier to use. It is also believed that before the Romans, the Etruscans were the civilization that used number symbols. And, in their system, they used “I”, “𐌡”, “𐌢”, and “𐌣” for representing “1”, “5”, “10”, and “50” respectively. Then, with slight changes Romans inducted the above into their system. In this system, seven English alphabets are used to represent the numbers used in maths.

  • The seven letters used are I, V, X, L, C, D, and M.
  • These alphabetical symbols are used in different arrangements to represent the numbers.

For Example:
The number 3 can be represented as III in Roman numerals.
But the number 4 can be represented as IV.

Roman Numerals (1 to 5)
Roman Numerals (1 to 5)

Every letter has a numeric value for example I represents 1, V represents 5, and so on.
The Roman numerals from 1 to 10 are represented as:

Roman Numerals (1 to 10)
Roman Numerals (1 to 10)

The limitation of this system of writing numbers is that it cannot handle large numbers. And becomes tedious to represent numbers beyond thousands.

Roman Numerals Symbol for Hindu-Arabic Number

The following Roman numbers hold a numeric value of Hindu-Arabic numbers. Mostly, these symbols are used in different arrangements for writing Roman numerals.

Roman SymbolArabic Number
Roman SymbolHindu-Arabic Number
I1C100
V5D500
X10M1000
L50
  • Bar on the alphabet represents the “value multiplied by 1000”.
    For Example,
    C has a value of 100
    Now, C with bar represents a value of 100 x 1000 = 100000.
  • There is no symbol for zero in this system.
  • In Romans “Nulla” was used for denoting zero.

 

Rules for assigning Roman Numerals

As mentioned, to assign Roman numerals for any numbers you have to follow certain rules. Further, the conversion of Roman numerals to Hindu- Arabic numbers also involves a set of rules. Some of the rules you can follow are as follows:

  • A symbol can be repeated almost three consecutive times in a number.I=1
    II=2
    III=3
    IIII= Nothing

    Symbols cannot be repeated 4 times.

    Similarly, XXX=30
    XXXX= Nothing
    XL= 40

 

  • Characters V, D, and L are never repeated.

 

  • When a symbol repeats consecutively then the value of the symbol is summed up.III= 1+1+1

    Hence, the Roman numeral representation of 3 is III.

    Similarly,
    XXX= 10+10+10

    Thus, you can represent 30 as XXX in Roman numeral format.

 

  • I, X, and C can only be subtracted. I can be subtracted from V and X while X can be subtracted from L, C, and M.IV= 5-1

    Thus, IV represents the number 4.

 

  • When a symbol of greater value succeeds the lower value symbol, then the lower value is subtracted from the higher value.For Example-IX, here “X” is a greater number and is succeeded by the smaller number “I”, hence addition. X-I=10-1=09

 

  • When a symbol of lower value succeeds the higher value symbol then the addition of the value of symbols takes place.For Example- XI, here the lower value Roman number “I” is succeeded by the higher value “X”, so the addition will take place.

    X+I=10+1=11

 

  • Bar above Roman numerals increases the value of the symbol by 1000. This rule is helpful to write numbers like 20000, 10000, 500000, etc in Roman numerals.

 

Representation of Hindu-Arabic Numbers into Roman Numerals

Arabic NumberRoman NumeralArabic NumberRoman Numeral
1I29XXIX
2II39XXXIX
3III49XLIX
4IV59LIX
5V69LXIX
6VI79LXXIX
7VII89LXXXIX
8VIII99XCIX
9IX499CDXCIX
10X999CMXCIX
50L9999I̅X̅CMXCIX
100C1000M
500D550DL
1000M1050ML
5000V̅5050
10000X̅
20000X̅X̅

Writing Hindu-Arabic Numbers into Roman Numerals

  • Step 1: Expand the Hindu-Arabic Number in such a way in you can assign the Roman value most comfortably.
  • Step 2: Assign the Roman Numerals independently and then club them together to represent the number.
  • Further, it’s important to remember the seven Roman Numbers and their equivalent Hindu-Arabic numbers.

You can try to understand the concepts and application of the rules discussed above with the help of these questions.

Example 1- Represent 9 in Roman numerals. Answer: 9=10-1, So IX
Rule: When a symbol of lower value is before the higher value symbol then the subtraction of the lower value takes place. For Example- IX, here the lower value Roman number “I” is before the higher value “X”.

Example 2- Represent 29 in Roman numerals. Answer: Step 1: First, Expand the number. 29=20+9 which can be further written as 10+10+9.
Step 2: Secondly, assign the Roman symbol independently to the expanded number. X+X+IX.
Thus,
The number 29 can be represented as XXIX in Roman numerals.

Example 3- Represent 301 as a Roman numeral. Answer: Step1: 301=300+1 Step2: CCC+I, Thus, 301=CCCI

Example 4- Represent 719 as a Roman numeral. Answer: Step1: 719=700+19 Step2: DCC+XIX, Thus, 719= DCCXIX

Example 5- Represent XXXV in Hindu-Arabic numeral.
Answer: X+X+X+V
The Roman number X has a value of 10.
Further, the Roman numeral V has a value of 5.
So, XXXV= 10+10+10+5
And, the value of XXXV is 35.
Rule: When a symbol repeats consecutively then the value of the symbol is summed up.

Example 6- What does the Roman number D represents?
Answer: The Roman number D has a value equivalent to 500.
Rule: The bar on the alphabet represents the “value multiplied by 1000”.
Thus, D has a value equivalent to 500 x 1000= 500000.
Try!
Can you represent 30000 as Roman numerals? Mention the rule used in this regard.

  • The Roman numeral system has its roots in ancient Rome and the Etruscan civilization.
  • Roman numerals do not have anything like zero.
  • There is no symbol to represent 0.

 

Roman numbers and word problems

Question: Raman has 30000 pens with him. His younger brother gave him 5000 more pens. Can you represent the total number of pens with Raman in Roman numbers?

Solution:
Bar Model Representation of the Problem:

Two parts are given and a whole is required.
An addition number sentence is required to solve this question.
30000+5000= 35000
Further, 3500 can be represented in Roman numerals following the rules learned above.
30000 can be represented as XXX with bar
5000 can be represented as V.
Hence, 35000 can be represented as XXXV.
Therefore, the total number of pens with Raman is XXXV.

Problems
Represent the Arabic Number into Roman Numbers:

  • 101
  • 99
  • 349
  • 451
  • 1001
  • 789
  • 898
  • 985
  • 100001
  • 11001

Answers:

  • 100+1 = C+I= CI
  • 90+9 = XC+IX = XCIX
  • 300+40+9 = CCC+XL+IX = CCCXLIX
  • 400+50+1 = CD+L+I = CDLI
  • 1000+1 = M+I = MI
  • 700+80+9 = DCC+LXXX+IX = DCCLXXXIX
  • 800+90+8 = DCCC+XC+VIII = DCCCXCVIII
  • 900+80+5 = CM+LXXX+V = CMLXXXV
  • 100000+1 = C+I = CI
  • 1100+1 = MC+I = MCI

Convert the Roman Numeral into a Hindu-Arabic Number:

  • DCCCXII
  • CMXXV
  • MCIX
  • MCC
  • CM
  • CDXXIX
  • DCXXXV
  • DCCC
  • DC
  • C

Answers:

  • 812
  • 925
  • 1109
  • 1200
  • 900
  • 429
  • 635
  • 800
  • 600
  • 100

Can you use any alphabet to write a Roman number?
Answer: No