CBSE Class 6 Mathematics Chapter 1: Knowing Your Numbers - NCERT Solutions

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CBSE Class 6 Mathematics Chapter 1, "Knowing Your Numbers," introduces students to the fascinating world of large numbers. This chapter delves into both the Indian and International systems of numeration, helping you understand how to read, write, and compare numbers of all sizes. You'll learn the proper use of commas to make large numbers easier to read and master the art of writing them in both figures and words. The solutions explore concepts like place value, covering units like lakhs and crores in the Indian system, and millions and billions in the International system. Each problem is explained step-by-step, ensuring you build a solid understanding of number sense. This foundational knowledge is essential for your continued success in mathematics and for tackling more complex problems in the future.

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BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 1

Chapter summary

Chapter 1, "Knowing Your Numbers," for CBSE Class 6 Mathematics introduces students to the fundamental concepts of large numbers. The NCERT Solutions cover exercises on filling in blanks to understand place value relationships (e.g., lakhs to ten thousands, millions to hundred thousands), placing commas correctly for Indian and International systems, and writing number names from numerals and vice versa. The solutions emphasize the distinct comma placement rules for the two systems, aiding students in accurate representation and reading of large numbers.

Learning outcomes

  • Understand the relationship between different place values in the Indian and International systems.
  • Correctly place commas in large numbers according to both Indian and International systems.
  • Write large numbers in words and figures using both numeration systems.
  • Convert between Indian and International number names and numerals.
  • Develop proficiency in reading and writing large numbers accurately.

Topics covered

Paper topics

  • Large Numbers
  • Indian System of Numeration
  • International System of Numeration
  • Place Value
  • Number Names
  • Writing Numerals
  • Comma Placement
  • Comparing Numbers
  • Lakh
  • Crore
  • Million
  • Billion

Important topics

  • Indian System of Numeration
  • International System of Numeration
  • Comma Placement Rules
  • Place Value Concepts
  • Writing Numbers in Words and Figures

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Questions and Solutions

Question 1

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

Solution:

To fill in the blanks, we need to understand the place value relationships in both the Indian and International systems of numeration.

  1. (a) 1 lakh = 10 ten thousand 1 lakh is equal to 1,00,000. One ten thousand is 10,000. To find how many ten thousands make a lakh, we divide: 1,00,000 / 10,000 = 10.
  2. (b) 1 million = 10 hundred thousand 1 million is equal to 1,000,000. One hundred thousand is 100,000. To find how many hundred thousands make a million, we divide: 1,000,000 / 100,000 = 10.
  3. (c) 1 crore = 10 ten lakh 1 crore is equal to 1,00,00,000. One ten lakh is 10,00,000. To find how many ten lakhs make a crore, we divide: 1,00,00,000 / 10,00,000 = 10.
  4. (d) 1 crore = 10 million 1 crore is 1,00,00,000. 1 million is 10,00,000. So, 1 crore = 10 x 10,00,000 = 10 million. Alternatively, 1 crore = 10,000,000. 1 million = 1,000,000. 10,000,000 / 1,000,000 = 10.
  5. (e) 1 million = 10 lakh 1 million is 1,000,000. 1 lakh is 1,00,000. To find how many lakhs make a million, we divide: 1,000,000 / 1,00,000 = 10.

Question 2

Place commas correctly and write the numerals for the following number names:

(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.

Solution:

We need to write the given number names in figures, using the correct comma placement for each system.

  1. (a) Seventy-three lakh seventy-five thousand three hundred seven In the Indian system: 73 lakh = 73,00,000; 75 thousand = 75,000; 307. Combining these gives 73,75,307. The commas are placed as 73,75,307.
  2. (b) Nine crore five lakh forty-one In the Indian system: 9 crore = 9,00,00,000; 5 lakh = 5,00,000; 41. Combining these gives 9,05,00,041. The commas are placed as 9,05,00,041.
  3. (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 commas are placed as 7,52,21,302.
  4. (d) Fifty-eight million four hundred twenty-three thousand two hundred two In the International system: 58 million = 58,000,000; 423 thousand = 423,000; 202. Combining these gives 58,423,202. The commas are placed as 58,423,202.
  5. (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 commas are placed as 23,30,010.

Question 3

Insert commas suitable and write the names according to the Indian system of numeration for the following numerals:

(a) 87595762

(b) 8546283

(c) 99900046

(d) 98432701

Solution:

We will insert commas according to the Indian system (from right to left: 3 digits, then 2 digits, then 2 digits) and then write the number names.

  1. (a) 87595762 Inserting commas: 8,75,95,762. Reading the number: Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two.
  2. (b) 8546283 Inserting commas: 85,46,283. Reading the number: Eighty-five lakh forty-six thousand two hundred eighty-three.
  3. (c) 99900046 Inserting commas: 9,99,00,046. Reading the number: Nine crore ninety-nine lakh forty-six. (Note: The thousands place is 00).
  4. (d) 98432701 Inserting commas: 9,84,32,701. Reading the number: Nine crore eighty-four lakh thirty-two thousand seven hundred one.

Question 4

Insert commas suitable and write the names according to the International system of numeration for the following numerals:

(a) 78921092

(b) 7452283

(c) 99985102

(d) 48049831

Solution:

We will insert commas according to the International system (from right to left: groups of 3 digits) and then write the number names.

  1. (a) 78921092 Inserting commas: 78,921,092. Reading the number: Seventy-eight million nine hundred twenty-one thousand ninety-two.
  2. (b) 7452283 Inserting commas: 7,452,283. Reading the number: Seven million four hundred fifty-two thousand two hundred eighty-three.
  3. (c) 99985102 Inserting commas: 99,985,102. Reading the number: Ninety-nine million nine hundred eighty-five thousand one hundred two.
  4. (d) 48049831 Inserting commas: 48,049,831. Reading the number: Forty-eight million forty-nine thousand eight hundred thirty-one.

Common mistakes

  • Confusing comma placement between Indian and International systems.
  • Incorrectly converting between number names and numerals.
  • Misunderstanding the place value of large numbers (e.g., lakh vs. million).
  • Errors in writing number names for large figures.

Revision tips

  • Practice placing commas for both Indian and International systems side-by-side to spot differences.
  • Write out number names for given numerals and vice versa multiple times.
  • Focus on understanding the 'lakh', 'crore', 'million', and 'billion' place values.
  • Use the provided examples to check your understanding of number conversions.

Practice MCQs

Q1. How many ten thousands are there in 1 lakh?

Q2. Which numeral represents 'Nine crore five lakh forty-one' in the Indian system?

Q3. How many lakhs are there in 1 million?

Q4. In the International system, what is the correct comma placement for 78921092?

Q5. What is the Indian system name for 9,99,00,046?

Frequently asked questions

What is the main focus of CBSE Class 6 Maths Chapter 1?

Chapter 1, 'Knowing Your Numbers,' focuses on understanding and correctly using large numbers, including their representation in both the Indian and International systems of numeration.

How do the Indian and International systems of numeration differ?

The primary difference lies in the naming of place values and the placement of commas. The Indian system uses lakhs and crores, with commas placed after every three digits from the right, then every two. The International system uses millions and billions, with commas consistently placed after every three digits from the right.

Are the solutions provided for both Indian and International number systems?

Yes, the NCERT Solutions cover exercises that require understanding and applying both the Indian system (using lakhs and crores) and the International system (using millions and billions).

How do these solutions help in exam preparation?

These solutions provide clear, step-by-step explanations for each problem, helping students understand the methods for placing commas, writing number names, and converting between figures and words, which are common exam topics.

What is the relationship between 1 lakh and 1 million?

1 million is equal to 10 lakh. This means that 1,000,000 in the International system corresponds to 10,00,000 in the Indian system.

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