CBSE Class 6 Mathematics Chapter 1: Knowing Our Numbers NCERT Solutions
CBSE Class 6 Mathematics Chapter 1, 'Knowing Our Numbers,' lays the groundwork for understanding numerical concepts. The NCERT Solutions delve into large numbers, focusing on the correct use of commas in both Indian and International systems of numeration for accurate place value representation. Students will practice writing numbers in words and numerals, and converting between units such as lakhs and millions. The solutions provide clear, step-by-step explanations to help students master these skills. This chapter is crucial for developing a strong number sense and building confidence in handling numerical data, preparing students effectively for future mathematical studies.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 6 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 1: Knowing Our Numbers |
Chapter summary
Chapter 1, 'Knowing Our Numbers,' focuses on essential number concepts for Class 6. The NCERT Solutions cover exercises related to large number representation, including filling in blanks for conversions between units like lakhs and thousands, and millions and hundreds of thousands. It also emphasizes the correct placement of commas and writing numerals for given number names, adhering to both the Indian and International systems of numeration. The solutions provide clear examples for converting between numeral and word forms.
Learning outcomes
- Understand the relationship between different units of large numbers (lakhs, millions, thousands).
- Correctly place commas in numbers according to the Indian system of numeration.
- Correctly place commas in numbers according to the International system of numeration.
- Write number names in words for given numerals using both Indian and International systems.
- Write numerals in figures for given number names using both Indian and International systems.
- Compare and convert between Indian and International number systems.
Topics covered
Paper topics
- Large Numbers
- Place Value
- Indian System of Numeration
- International System of Numeration
- Commas in Numbers
- Writing Numbers in Words
- Writing Numbers in Figures
- Conversion of Units (Lakhs, Millions, Thousands)
Important topics
- Indian System of Numeration
- International System of Numeration
- Correct placement of commas
- Writing numbers in words and figures
- Understanding large number units (lakhs, millions)
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Questions and Solutions
Question 1: Fill in the blanks:
Fill in the blanks:
(a) 1 lakh = _____ ten thousand
(b) 1 million = _____ hundred thousand
(c) 1 crore = _____ ten lakh
(d) 1 crore = _____ million
(e) 1 million = _____ lakh
To fill in the blanks, we need to understand the relationship between different units of numbers:
- (a) 1 lakh = 10 ten thousand Explanation: 1 lakh = 1,00,000. One ten thousand = 10,000. Since 1,00,000 / 10,000 = 10, we have 1 lakh = 10 ten thousands.
- (b) 1 million = 10 hundred thousand Explanation: 1 million = 1,000,000. One hundred thousand = 1,00,000. Since 1,000,000 / 1,00,000 = 10, we have 1 million = 10 hundred thousands.
- (c) 1 crore = 10 ten lakh Explanation: 1 crore = 1,00,00,000. One ten lakh = 10,00,000. Since 1,00,00,000 / 10,00,000 = 10, we have 1 crore = 10 ten lakhs.
- (d) 1 crore = 10 million Explanation: 1 crore = 1,00,00,000. 1 million = 10,00,000. To convert crores to millions, we can use the relationship: 1 crore = 100 lakhs and 1 million = 10 lakhs. So, 1 crore = 100 lakhs = 10 x 10 lakhs = 10 million.
- (e) 1 million = 10 lakh Explanation: 1 million = 1,000,000. 1 lakh = 1,00,000. Since 1,000,000 / 1,00,000 = 10, we have 1 million = 10 lakhs.
Question 2: Place commas correctly and write the numerals:
Place commas correctly and write the numerals:
(a) Seventy-three lakh seventy-five thousand three hundred seven.
(b) Nine crore five lakh forty-one.
(c) Seven crore fifty-two lakh twenty-one thousand three hundred two.
(d) Fifty-eight million four hundred twenty-three thousand two hundred two.
(e) Twenty-three lakh thirty thousand ten.
We will place commas and write the numerals according to the Indian system (for a, b, c, e) and the International system (for d).
- (a) Seventy-three lakh seventy-five thousand three hundred seven In the Indian system, commas are placed after the third digit from the right, and then after every two digits. So, 73 lakh = 73,00,000; 75 thousand = 75,000; 307. Combining these gives 73,75,307. The numeral is 73,75,307.
- (b) Nine crore five lakh forty-one In the Indian system: 9 crore = 9,00,00,000; 5 lakh = 5,00,000; forty-one = 41. Combining these gives 9,05,00,041. The numeral is 9,05,00,041.
- (c) Seven crore fifty-two lakh twenty-one thousand three hundred two In the Indian system: 7 crore = 7,00,00,000; 52 lakh = 52,00,000; 21 thousand = 21,000; 302. Combining these gives 7,52,21,302. The numeral is 7,52,21,302.
- (d) Fifty-eight million four hundred twenty-three thousand two hundred two In the International system, commas are placed after every three digits from the right. 58 million = 58,000,000; 423 thousand = 423,000; 202. Combining these gives 58,423,202. The numeral is 58,423,202.
- (e) Twenty-three lakh thirty thousand ten In the Indian system: 23 lakh = 23,00,000; 30 thousand = 30,000; 10. Combining these gives 23,30,010. The numeral is 23,30,010.
Question 3: Insert commas suitable and write the names according to Indian system of numeration:
Insert commas suitable and write the names according to Indian system of numeration:
(a) 87595762
(b) 8546283
(c) 99900046
(d) 98432701
We will insert commas according to the Indian system (after every two digits from the right, except for the first group of three digits) and then write the number names.
- (a) 87595762 Inserting commas: 8,75,95,762. Reading the number: 8 crore, 75 lakh, 95 thousand, 762. The name is: Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two.
- (b) 8546283 Inserting commas: 85,46,283. Reading the number: 85 lakh, 46 thousand, 283. The name is: Eighty-five lakh forty-six thousand two hundred eighty-three.
- (c) 99900046 Inserting commas: 9,99,00,046. Reading the number: 9 crore, 99 lakh, 46. The name is: Nine crore ninety-nine lakh forty-six.
- (d) 98432701 Inserting commas: 9,84,32,701. Reading the number: 9 crore, 84 lakh, 32 thousand, 701. The name is: Nine crore eighty-four lakh thirty-two thousand seven hundred one.
Question 4: Insert commas suitable and write the names according to International system of numeration:
Insert commas suitable and write the names according to International system of numeration:
(a) 78921092
(b) 7452283
(c) 99985102
(d) 48049831
We will insert commas according to the International system (after every three digits from the right) and then write the number names.
- (a) 78921092 Inserting commas: 78,921,092. Reading the number: 78 million, 921 thousand, 092. The name is: Seventy-eight million nine hundred twenty-one thousand ninety-two.
- (b) 7452283 Inserting commas: 7,452,283. Reading the number: 7 million, 452 thousand, 283. The name is: Seven million four hundred fifty-two thousand two hundred eighty-three.
- (c) 99985102 Inserting commas: 99,985,102. Reading the number: 99 million, 985 thousand, 102. The name is: Ninety-nine million nine hundred eighty-five thousand one hundred two.
- (d) 48049831 Inserting commas: 48,049,831. Reading the number: 48 million, 049 thousand, 831. The name is: Forty-eight million forty-nine thousand eight hundred thirty-one.
Common mistakes
- Confusing the placement of commas between the Indian and International systems.
- Errors in writing number names, especially for large numbers with many zeros.
- Incorrectly converting between units like lakhs and millions.
- Misinterpreting place values in large numbers.
Revision tips
- Practice placing commas for at least 10-15 numbers in both systems.
- Write out number names for given numerals and vice-versa, focusing on large numbers.
- Create your own conversion problems between lakhs and millions to test understanding.
- Review the place value charts for both Indian and International systems side-by-side.
Practice MCQs
Q1. How many thousands are there in one lakh?
Explanation: One lakh is equal to 1,00,000. This can be written as 100 x 1,000, so there are 100 thousands in one lakh.
Q2. Which number represents 'Nine crore five lakh forty-one' in the Indian system?
Explanation: In the Indian system, commas are placed after the third digit from the right, and then every two digits. Nine crore is 9,00,00,000, five lakh is 5,00,000, and forty-one is 41. Combining these gives 9,05,00,041.
Q3. How is 78,921,092 written in words according to the International system?
Explanation: In the International system, commas are placed every three digits from the right. 78,921,092 is read as seventy-eight million (78), nine hundred twenty-one thousand (921), and ninety-two (092).
Q4. What is 1 million equal to in lakhs?
Explanation: 1 million is equal to 1,000,000. One lakh is 1,00,000. Therefore, 1,000,000 / 1,00,000 = 100. So, 1 million equals 100 lakhs.
Q5. In the Indian system, the number 99900046 is written as:
Explanation: For the Indian system, commas are placed after the first three digits from the right, and then after every two digits. Thus, 99900046 becomes 9,99,00,046.
Frequently asked questions
What is the main focus of Chapter 1: Knowing Our Numbers for Class 6 Maths?
This chapter focuses on understanding and representing large numbers, including the correct use of place value, commas, and writing numbers in words and figures according to both the Indian and International systems of numeration.
How do the NCERT Solutions help students with this chapter?
The solutions provide step-by-step explanations for each question, clarifying concepts like comma placement and number naming in different systems. They help students practice and build confidence in handling large numbers.
What is the difference between the Indian and International systems of numeration?
The primary difference lies in the naming of large numbers and the placement of commas. The Indian system uses lakhs and crores, with commas placed after every two digits after the first three, while the International system uses millions and billions, with commas placed after every three digits.
Are there exercises on converting between units like lakhs and millions?
Yes, the solutions cover exercises that involve understanding the relationship between different units, such as converting between lakhs and thousands, or millions and lakhs, to help students grasp the scale of large numbers.
How can I use these solutions to prepare for exams?
You can use these solutions to understand the methods for solving problems, practice the exercises thoroughly, and check your answers. Focusing on the common mistakes highlighted can also help you avoid errors during the exam.
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