Mathematics Class 5 - Number Names-And-Number-Sense Notes

Number Names and Number Sense

Welcome to the first chapter of your mathematics journey in Class 5: Number Names and Number Sense. This chapter is designed to help you build a strong foundation in understanding numbers, their names, and how to work with them in various ways. By the end of this chapter, you will be able to read, write, compare, and order large numbers, understand their place values, and use this knowledge to solve real-life problems. Let’s dive in!

Introduction

Numbers are everywhere in our daily lives. From counting objects, reading time, handling money, to measuring distances, numbers play a crucial role. But numbers are not just about counting; they have names, values, and properties that help us understand the world better. In this chapter, we will explore the fascinating world of numbers, learn how to read and write them in words, and develop a sense of how big or small a number is.

Key Concepts

• Reading and writing numbers up to 8 digits: Learn how to read and write numbers in both numerals and words, up to crores.
• Place value and face value: Understand the difference between the place value and face value of a digit in a number.
• Comparing and ordering numbers: Learn how to compare two or more numbers and arrange them in ascending or descending order.
• Forming numbers with given digits: Practice creating the largest and smallest numbers using a set of digits.
• Rounding off numbers: Learn how to round numbers to the nearest ten, hundred, thousand, etc.
• Estimation: Use estimation to quickly find approximate answers to mathematical problems.
• International and Indian Number Systems: Understand the difference between these two systems and how to read numbers in both.

1. Reading and Writing Large Numbers

In Class 5, you will work with numbers up to 8 digits. Let’s understand how to read and write these numbers in both numerals and words.

Indian Number System

In the Indian system, numbers are grouped as ones, tens, hundreds, thousands, lakhs, and crores. For example:

• 1,23,45,678 is read as One crore twenty-three lakh forty-five thousand six hundred seventy-eight.
• 7,20,154 is read as Seven lakh twenty thousand one hundred fifty-four.

International Number System

In the International system, numbers are grouped as ones, tens, hundreds, thousands, millions, and billions. For example:

• 12,345,678 is read as Twelve million three hundred forty-five thousand six hundred seventy-eight.
• 720,154 is read as Seven hundred twenty thousand one hundred fifty-four.

Practice:

• Write 5,67,890 in words in both Indian and International systems.
• Write the numeral for “Nine lakh fifty thousand two hundred one”.

2. Place Value and Face Value

Place value is the value of a digit based on its position in a number. Face value is the actual value of the digit itself.

• In 4,52,316, the place value of 5 is 50,000, but its face value is 5.
• In 7,20,154, the place value of 2 is 20,000, but its face value is 2.

Expanded Form

Writing a number in expanded form means expressing it as the sum of the place values of its digits. For example:

• 4,52,316 = 4,00,000 + 50,000 + 2,000 + 300 + 10 + 6
• 7,20,154 = 7,00,000 + 20,000 + 100 + 50 + 4

Practice:

• Write the expanded form of 3,45,678.
• What is the place value and face value of 6 in 6,78,901?

3. Comparing and Ordering Numbers

To compare numbers, start from the leftmost digit. The number with the greater digit in the highest place is larger.

• 98,765 > 89,765 because 9 (ten thousands) > 8 (ten thousands).
• Arrange in ascending order: 45,321; 54,123; 43,512.
  Answer: 43,512; 45,321; 54,123

Practice:

• Which is greater: 7,20,154 or 7,02,154?
• Arrange in descending order: 1,23,456; 1,32,456; 1,23,654.

4. Forming Numbers with Given Digits

You can form the largest or smallest number using a set of digits. For the largest number, arrange the digits in descending order; for the smallest, arrange them in ascending order.

• Given digits: 3, 7, 1, 9, 5
  Largest number: 97531
  Smallest number: 13579

Practice:

• Form the largest and smallest 5-digit numbers using 2, 8, 0, 6, 4.
• Form the largest and smallest 6-digit numbers using 9, 3, 1, 7, 5, 2.

5. Rounding Off Numbers

Rounding off means making a number simpler but keeping its value close to what it was. We round numbers to the nearest ten, hundred, thousand, etc.

• Round 4,567 to the nearest hundred: 4,600
• Round 7,892 to the nearest thousand: 8,000

Rules for Rounding Off

If the digit to the right is less than 5, round down. If the digit to the right is 5 or more, round up.

Practice:

• Round 3,849 to the nearest hundred.
• Round 6,275 to the nearest thousand.

6. Estimation

Estimation helps us find approximate answers quickly. It is useful in daily life, such as estimating the total cost while shopping or the distance to a place.

• Estimate the sum: 4,567 + 3,892 (Round both numbers to the nearest thousand: 5,000 + 4,000 = 9,000)
• Estimate the difference: 7,892 - 2,345 (Round both numbers to the nearest thousand: 8,000 - 2,000 = 6,000)

Practice:

• Estimate the sum: 2,345 + 6,789
• Estimate the difference: 9,876 - 4,321

7. International and Indian Number Systems

The Indian and International number systems use different ways to group digits and name large numbers. Understanding both systems is important as you may encounter both in textbooks and daily life.

Number	Indian System	International System
1,00,000	One Lakh	One Hundred Thousand
10,00,000	Ten Lakh	One Million
1,00,00,000	One Crore	Ten Million

Practice:

• Write 5,00,000 in the International system.
• Write 2,000,000 in the Indian system.

8. Real-Life Applications

Understanding number names and number sense is not just for exams. It helps you in real life, such as:

• Reading population figures in newspapers
• Understanding distances on maps
• Handling money and making purchases
• Reading electricity and water bills
• Comparing scores in sports

Summary

Numbers can be written in numerals and words. Place value and face value help us understand the value of digits in a number. We can compare, order, and round numbers for various purposes. Both Indian and International number systems are important to know.

Practice Questions

Try to solve these questions to test your understanding of the chapter.

1. Write the number name for 7,20,154 in both Indian and International systems.
2. What is the place value of 3 in 3,45,678?
3. Arrange in ascending order: 45,321; 54,123; 43,512.
4. Form the largest and smallest 5-digit numbers using 2, 8, 0, 6, 4.
5. Round 3,849 to the nearest hundred.
6. Estimate the sum: 2,345 + 6,789.
7. Write 5,00,000 in the International system.
8. Write 2,000,000 in the Indian system.
9. Write the expanded form of 4,52,316.
10. Compare: Which is greater, 7,20,154 or 7,02,154?

Challenge Yourself

Try these activities to apply your knowledge:

• Find the population of your city or state and write it in both Indian and International number systems.
• Ask your parents for the electricity bill and read the numbers in words.
• Make a list of numbers you see around you and write their number names.

Did You Know?

The largest number with 8 digits is 9,99,99,999 (Indian system) or 99,999,999 (International system). Zero was invented in India! The word “lakh” is used in India, Bangladesh, Nepal, and Sri Lanka, but not in the International system.

Glossary

• Numeral: A symbol or group of symbols representing a number.
• Place Value: The value of a digit depending on its position in a number.
• Face Value: The value of the digit itself.
• Ascending Order: Arranging numbers from smallest to largest.
• Descending Order: Arranging numbers from largest to smallest.
• Rounding Off: Making a number simpler but keeping its value close to what it was.
• Estimation: Finding an approximate value.

Answers to Practice Questions

1. 7,20,154: Indian – Seven lakh twenty thousand one hundred fifty-four; International – Seven hundred twenty thousand one hundred fifty-four.
2. Place value of 3 in 3,45,678 is 3,00,000.
3. Ascending order: 43,512; 45,321; 54,123.
4. Largest: 86420; Smallest: 20468.
5. 3,849 rounded to the nearest hundred is 3,800.
6. Estimate: 2,345 ≈ 2,000; 6,789 ≈ 7,000; Sum ≈ 9,000.
7. 5,00,000 in International system: Five hundred thousand.
8. 2,000,000 in Indian system: Twenty lakh.
9. 4,52,316 = 4,00,000 + 50,000 + 2,000 + 300 + 10 + 6.
10. 7,20,154 is greater than 7,02,154.

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Keep practicing and exploring numbers around you. The more you work with numbers, the stronger your number sense will become!