Class 5 Maths Chapter 1 Notes: Understanding Large Numbers

Mathematics forms the foundation of logical thinking, and in Class 5, students begin their journey into understanding large numbers, place values, and fundamental arithmetic operations with them. Chapter 1 of Class 5 Mathematics primarily focuses on large numbers, their operations, and their applications in daily life.

1. Understanding Large Numbers

In earlier classes, students learned about numbers up to thousands and ten thousands. In Class 5, they explore numbers up to lakhs and crores (Indian System) and millions and billions (International System).

1.1 Place Value System

The place value system helps in understanding the worth of a digit based on its position in a number.

Indian Place Value System

In the Indian number system, we use lakhs and crores instead of millions and billions.

Place	Ones	Tens	Hundreds	Thousands	Ten Thousands	Lakhs	Ten Lakhs	Crores
Example	5	2	1	4	3	9	7	6

Example: 97,43,215 is read as Ninety-seven lakh forty-three thousand two hundred fifteen.

International Place Value System

The International system follows a different pattern, using millions and billions.

Place	Ones	Tens	Hundreds	Thousands	Ten Thousands	Hundred Thousands	Millions	Billions
Example	2	5	3	6	9	8	7	1

Example: 7,865,432 is read as Seven million eight hundred sixty-five thousand four hundred thirty-two.

1.2 Reading and Writing Large Numbers

• Indian System: 25,43,128 is read as Twenty-five lakh forty-three thousand one hundred twenty-eight.
• International System: 2,543,128 is read as Two million five hundred forty-three thousand one hundred twenty-eight.

1.3 Comparing Numbers

To compare two large numbers:

1. Count the number of digits.
2. The number with more digits is greater.
3. If the number of digits is the same, compare digits from left to right.

Example:

• 98,32,415 > 9,45,732 (since the first number has 7 digits while the second has only 6 digits).

2. Operations on Large Numbers

2.1 Addition and Subtraction

Steps for Addition:

1. Write the numbers in column format, aligning the digits according to their place values.
2. Add from right to left (ones place to highest place).
3. Carry forward if the sum exceeds 9.

Example:

markdown

   4,32,875
+  3,45,928
------------
   7,78,803

Steps for Subtraction:

1. Align numbers according to place values.
2. Subtract from right to left.
3. Borrow if necessary.

Example:

markdown

   8,92,745
-  4,57,328
------------
   4,35,417

2.2 Multiplication of Large Numbers

Steps:

1. Multiply the numbers just like smaller numbers.
2. Write each intermediate product correctly aligned.
3. Add all intermediate products.

Example:

  3,245 × 12
= (3,245 × 10) + (3,245 × 2)
= 32,450 + 6,490
= 38,940

2.3 Division of Large Numbers

Division follows the standard method:

1. Divide the first digit or set of digits by the divisor.
2. Write the quotient.
3. Multiply and subtract.
4. Bring down the next digit and repeat until completion.

Example:

  78,432 ÷ 12 = 6,536

3. Rounding Off Large Numbers

To estimate numbers, we round them off to the nearest tens, hundreds, thousands, etc.:

1. Check the digit at the rounding place.
2. If it is 5 or more, increase the preceding digit by 1.
3. If it is less than 5, keep the preceding digit the same and change the following digits to 0.

Example:

• 4,37,894 rounded to the nearest thousand = 4,38,000
• 4,37,894 rounded to the nearest lakh = 4,40,000

4. Roman Numerals

In addition to learning large numbers, students also revisit Roman numerals.

Number	Roman Numeral
1	I
5	V
10	X
50	L
100	C
500	D
1000	M

Rules for Writing Roman Numerals

1. Repetition increases value (e.g., XX = 20).
2. A smaller number before a larger one means subtraction (e.g., IX = 9).
3. A smaller number after a larger one means addition (e.g., VI = 6).

5. Applications in Real Life

• Reading population statistics (e.g., India’s population is 1.4 billion).
• Understanding currency values (e.g., Indian rupee denominations).
• Measurement units (e.g., distance between cities in kilometers).
• Bank transactions (e.g., handling amounts in lakhs and crores).

FAQs on Class 5 Maths Chapter 1

1. What is the difference between the Indian and International Number Systems?

The Indian system uses lakhs and crores, while the International system uses millions and billions.

2. How do I compare large numbers?

Compare the number of digits; if equal, compare digit by digit from left to right.

3. What is the place value of 5 in 5,46,738?

It is 5 lakh (5,00,000) in the Indian system.

4. How do we round off numbers?

Check the digit at the rounding place. If 5 or more, increase the preceding digit by 1.

5. What is the Roman numeral for 49?

49 = XLIX (40 + 9).