Roman Numerals Class 5 Notes Maths

What are Roman Numerals?

• Romans developed a different system of numeration about 2000 years ago, known as Roman numerals.
• The ancient Romans explained that when a number reaches 10 it is not easy to count on one’s fingers. Therefore, there was a need to create a proper number system that could be used for trade and communications. 
• Roman numerals are denoted using a different combination of symbols that include the English alphabet. 
• There are seven basic Roman Numerals: I, V, X, L, C, D, M.
• These numerals and their corresponding Hindu-Arabic numerals are given below.

Seven Basic Roman Numerals

Did You Know
In the Roman numeral , system there is no symbol for zero.

Large Roman Numerals

Large numbers in Roman numerals 

Chart of Roman Numerals from 1 to 10,000

Rules to Write Roman Numerals

Roman Numerals Chart 

Rule 1: Repetition Rule

When a letter is used more than once, we add its value each time to get the number.

Did You Know:
1. The same roman numeral cannot be repeated more than 3 times together.
Example: We represent 3 as III in Roman numerals but we cannot represent 4 as IIII; it is written as IV.
2. The symbols V, L and D are never repeated.

Examples: 
II = 1 + 1 = 2
XXX = 10 + 10 + 10 = 30
CCC = 100 + 100 + 100  = 300
MM = 1000 + 1000 = 2000
MMM = 1000 + 1000 + 1000 = 3000

Rule 2: Addition Rule

When a smaller number comes after a larger one, you add both of the numbers.

Examples: 
VII = 5 + 1 + 1 = 7
XII = 10 + 1 + 1 = 12
XXVII = 10 + 10 + 5 + 1 + 1 = 27
LVII = 50 + 5 + 1 + 1= 57
LXVI = 50 + 10 + 5 + 1 = 66
CVII = 100 + 5 + 1 + 1 = 107
CLXV = 100 + 50 + 10 + 5 = 165
DC = 500 + 100 = 600
MDCXVIII = 1000 + 500 + 100 + 10 + 5 + 1 + 1 + 1 = 1618

Rule 3: Subtraction Rule

When a smaller number comes before a larger one, you subtract.

Examples: 
IV = 5 – 1 = 4
IX = 10 – 1 = 9
XL = 50 – 10 = 40
XC = 100 – 10 = 90
CD = 500 – 100 = 400
CM = 1000 – 100 = 900

Tips:

• V, L, and D are never subtracted.
• I can be subtracted from V and X only once. 
• X can be subtracted from L and C only once. 
• C can be subtracted from D and M only once. 
• Thus, I or V is never written to the left of L or C. L is never written to the left of C.

Rule 4: Bar Rule

1000 can be represented by a line on the letter, which is called a bar.

Example:

Roman Numbers 1 to 100

Conversion

We will follow the following steps to convert from Roman Numerals to Arabic Numerals or vice versa.

I. Convert Hindu Arabic to Roman Numeral

Suppose , we have to convert 72 into Roman Numerals.

Step 1: Break down 72 into largest possible tens and ones according to roman numerals:
72 = 50 + 20 + 2 

Step 2: Convert each part to Roman numerals:
50 = L
20 = XX
2 = II

Step 3: Combine the parts:
72 = LXXII

II. Convert Roman Numeral to Hindu-Arabic Numeral

Suppose, We have to convert XII into a number.

Step 1: Write values of the given Roman Numerals
X = 10
II = 2

Step 2: Add the Values
10 + 2 = 12

Answer: XII = 12

Solved Examples

Example 1: Convert 45 to Roman Numerals

Sol: Step 1: Break down the number into largest tens and ones according to roman numerals that fits into that number:
45 can be broken down into: 
45 = 40+5
Step 2: Write Each Part as Roman Numerals
40 = XL(Subtraction Rule used, 40 = 50-10)
5= V
Step 3: Combine the Roman Numerals
After combining, we get : XL+V = XLV

Example 2: Convert 789 to Roman Numerals

Sol: Step 1: Break Down the Number

789 can be broken down into:

789 = 700+ 80 +9

Step 2: Write Each Part as Roman Numerals

700 = DCC (Addition rule used, 700 = 500+200)

80 = LXXX (Addition rule used,80=50+30)

9 = IX (Subtraction Rule used,9=10-1)

Step 3: Combine the Roman Numerals

After combining, we get: DCC + LXXX + IX = DCCLXXXIX

Example 3: Convert XLII to Hindu-Arabic Numerals

Sol: Step 1: Break Down the Roman Numerals
XL = 40 (This uses the subtraction rule: X before L means 50 - 10 = 40)
II = 2
Step 2: Add the Values
40 + 2 = 42
Answer: XLII = 42

Example 4: Convert CDXLIV to Hindu-Arabic Numerals

Sol: Step 1: Break Down the Roman Numerals
CD = 400 (C before D means 500 - 100 = 400)

XL = 40 (X before L means 50 - 10 = 40)

IV = 4 (I before V means 5 - 1 = 4)
Step 2: Add the Values
400 + 40 + 4 = 444
Answer: CDXLIV = 444