Roman Numerals Class 5 Notes Maths

In Roman Numerals, we will be learning about a number system that uses letters to represent mathematical values. 
They are on movie titles, video games, and even on clocks.

We will discuss the basic letters and rules for combining them to form different numbers. Let’s jump in and start learning!

What are Roman Numerals?

• Romans developed a different system of numeration about 2000 years ago, known as Roman numerals.
• Roman numerals are a system of numbers that use letters to represent values.
  
• There are seven basic roman numerals i.e I ,V, X, L, C, D, M. 
• We can write any Hindu-Arabic numeral using these seven letters(Except zero).
• Below are the Roman numerals and their corresponding Hindu-Arabic numerals.

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

Rules to Write Roman Numerals

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.

Example 1: Convert 300 into Roman Numerals.

Sol: 300 = 100 + 100 + 100
= C + C + C 
=CCC

Example 2: Convert II , XXX, CCC in Hindu Arabic Numerals.

Sol:  II = 1+1 = 2
XXX = 10+10+10 = 30
CCC = 100 + 100+ 100 = 300

Rule 2: Addition Rule

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

Example 1: Convert 60 into Roman numbers

Sol: 60 = 50+10
= L + X 
= LX

Example 2: Convert VI into Hindu- Arabic Numerals.

Sol: We know that,
V = 5 and I = 1.
This implies a smaller number (I) comes after a larger one (V), therefore we will add them
VI = 5+1 = 6

Rule 3: Subtraction Rule

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

Example 1: Convert 400 into Roman Numeral

Sol: 400 = 500 - 100
500 = D
100 = C
400 = CD ( When a smaller number comes before a larger one, you subtract.)

Example 2: Convert IV into Hindu- Arabic Numerals

Sol: We know that,
V = 5 and I = 1.
This implies a larger number (V) comes after a smaller one (I), therefore we will subtract them.
IV = 5-1 = 4

Rule 4: Bar Rule

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

Example:

Conversion

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

In the following example we will first understand how to 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

Now we will understand how we can 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

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