Table of Contents
NCERT Solutions for Class 6 Maths Chapter 1 – Knowing Our Numbers
NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers is a vital resource for 6th-grade students beginning their mathematical journey. lass 6 Maths Chapter 1 establishes the foundation for understanding numbers and their properties, which is crucial for grasping more advanced mathematical concepts in later grades. The chapter covers topics included in CBSE syllabus such as large numbers, place value, comparing numbers, using commas in large numbers, expanding numbers, and rounding numbers to the nearest tens, hundreds, and thousands. These fundamental concepts are essential for students as they are the building blocks for more complex mathematical operations and problem-solving.
Created by experienced Maths teachers, Infinity larn’s NCERT Solutions for Class 6 Maths Chapter 1 provides clear explanations and numerous practice questions. It allows students to learn at their own pace and master the concepts necessary for excelling in their exams. These NCERT solutions are accessible for download on the Infinity learn website, where students can also get NCERT Solutions Class 6 Science to further enhance your academic performance.
NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers PDF Download
Get comprehensive understanding of basic number concepts with the NCERT Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers. PDF of NCERT solutions for class 6 Maths chapter 1 resource is crafted by expert Maths teachers to help you grasp the fundamentals of large numbers, place values, rounding off numbers, and more. Perfect for self-paced learning and thorough practice, these solutions are designed to boost your confidence and performance in exams.
Also Check: CBSE Syllabus for Class 6 Maths
Topics Covered in Class 6 Maths Chapter 1 Knowing Our Number
1.1 Introduction
This section acquaints students with the notion of counting and representation of large numbers. It provides historical insight into how numerical systems have developed and underscores the importance of numbers in various contexts.
1.2 Comparing Numbers
The chapter progresses to comparing numbers, where students engage with exercises designed to recognize the greatest and smallest numbers in a set. They also dive into the concept of place values and how these determine the size of a number.
- 1.2.1 How Many Numbers Can You Make? This part invites students to explore permutations of numbers to understand which combinations produce the largest or smallest possible numbers.
- 1.2.2 Shifting of Numbers: Students learn the effects of changing the order of digits within a number and how this can affect its value.
- 1.2.3 Introducing 10,000: The concept of five-digit numbers is introduced here, laying down the foundation for understanding the base-10 system.
- 1.2.4 Revisiting Place Value: This reinforces the place value system for numbers, extending to five-digit numbers, which is essential for comprehending the number system.
- 1.2.5 Introducing 1,00,000: Six-digit numbers are discussed, with emphasis on the numerical term ‘lakh’, a critical milestone in the Indian number system.
- 1.2.6 Larger Numbers: The journey of numbers continues as the chapter expands on the idea of creating and understanding numbers beyond lakhs.
- 1.2.7 An Aid in Reading and Writing Large Numbers: This subsection provides students with tools and methods to read and write large numbers effectively, using place values and commas.
1.3 Large Numbers in Practice: Practical applications of large numbers are showcased here, from estimating the number of grains in a sack to the population of a city.
- 1.3.1 Estimation: Teaches students how to estimate large numbers and make informed guesses.
- 1.3.2-1.3.7 Estimating to the Nearest Tens, Hundreds, and Thousands by Rounding Off: Students learn rounding off numbers to the nearest ten, hundred, and thousand, which is a useful skill in everyday calculations.
1.4 Using Brackets: This concept introduces the hierarchy in operations, teaching students the correct order to solve mathematical expressions.
1.5 Roman Numerals: The chapter wraps up with an introduction to Roman numerals, adding historical context to the number system and providing a different perspective on numerical representation.
NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers All Exercise
NCERT solutions for class 6 Maths chapter 1 Knowing Our Numbers cover the 3 exercises which are exercise 1.1, exercise 1.2, and exercise 1.3.
NCERT Solutions for Class 6 Chapter 1 Knowing Our Numbers Exercise 1.1
Here is the NCERT solutions for class 6 Maths exercise 1.1 textbook questions on Page No. 12
1. Fill in the blanks:
(a) 1 lakh = ………….. ten thousand.
(b) 1 million = ………… hundred thousand.
(c) 1 crore = ………… ten lakhs.
(d) 1 crore = ………… million.
(e) 1 million = ………… lakhs.
Sol.
(a) 1 lakh =ten ten thousand.
(b) 1 million ten hundred thousand.
(c) 1 crore ten ten lakh
(d) 1 crore ten million
(e) 1 million ten lakh
2. 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
Sol.
(a) 73,75,307
(b) 9,05,41,000
(c) 7,52,21,302
(d) 58,423,202
(e) 23,30,010
3. Insert commas suitably and write the names according to the Indian System of Numeration:
(a) 87595762
(b) 8546283
(c) 99900046
(d) 98432701
Sol.
(a) 8,75,95,762
(b) 85,46,283
(c) 9,99,00,046
(d) 9,84,32,701
4. Insert commas suitably and write the names according to the International System of Numeration:
(a) 78921092
(b) 7452283
(c) 99985102
(d) 48049831
Sol.
(a) 78,921,092
(b) 7,452,283
(c) 99,985,102
(d) 48,049,831
NCERT Solutions for Class 6 Chapter 1 Knowing Our Numbers Exercise 1.2
Below is the simple and easy to understand NCERT solutions for class 6 Maths exercise 1.2 textbook questions on Page No. 16
1. A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third, and final day was respectively 1094, 1812, 2050, and 2751. Find the total number of tickets sold on all four days.
Sol.
Number of tickets sold on the first day – 1094
Number of tickets sold on the second day – 1812
Number of tickets sold on the third day – 2050
Number of tickets sold on the final day – 2751
Total number of tickets sold on all the four days 1094 +1812 +2050 + 2751 = 7707.
2. Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?
Sol.
Let
be the additional runs needed.
Given that Shekhar has already scored 6980 runs and wishes to complete 10,000 runs, we can write the equation:
Subtracting 6980 from both sides, we get:
So, Shekhar needs to score 3020 more runs to reach his goal of 10,000 runs.
3. In an election, the successful candidate registered 5,77,500 votes, and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?
Sol.
Margin of victory = Votes secured by the successful candidate – Votes secured by the rival
Margin of victory = 577,500 – 348,700
Margin of victory = 228,800 votes
Therefore, the successful candidate won the election by 228,800 votes.
4. Kirti bookstore sold books worth Rs 2,85,891 in the first week of June and books worth Rs 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?
Sol.
Total sale for both weeks = Sale in the first week + Sale in the second week
Total sale for both weeks = Rs 285,891 + Rs 400,768
Total sale for both weeks = Rs 686,659
The sale was greater in the second week.
Difference in the sale in both weeks = Sale in the second week – Sale in the first week
Difference in the sale = Rs 400,768 – Rs 285,891
Difference in the sale = Rs 114,877
Therefore, the sale in the second week was greater by Rs 114,877 than in the first week.
5. Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, and 3 each only once.
Sol.
Greatest 5-digit number = 76,432
Least 5-digit number = 23,467
Difference between the two numbers = 76,432 – 23,467
Difference between the two numbers = 52,965
Therefore, the difference between the greatest and the least 5-digit number is 52,965.
6. A machine, on average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
Sol.
Number of screws manufactured in January = Number of screws manufactured in a day x Number of days in January
Number of screws manufactured in January = 2,825 x 31
Number of screws manufactured in January = 87,575
Therefore, the machine produced 87,575 screws in January 2006.
7. A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after the purchase?
Sol.
Total cost of purchasing radio sets = Number of radio sets x Cost per radio set
Total cost of purchasing radio sets = 40 x Rs 1,200
Total cost of purchasing radio sets = Rs 48,000
Money remaining with the merchant = Total money – Total cost of purchasing radio sets
Money remaining with the merchant = Rs 78,592 – Rs 48,000
Money remaining with the merchant = Rs 30,592
Therefore, money remaining with the merchant after purchasing radio sets is Rs 30,592.
8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?
Sol.
Difference between the multipliers = 65 – 56 = 9
Difference between the student’s answer and the correct answer = 7,236 x 9
Difference between the answers = 65,124
Therefore, the student’s answer was greater than the correct answer by 65,124.
9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain?
Sol.
Total length of cloth in cm = Total length of cloth x 100
Total length of cloth in cm = 40 x 100 = 4000 cm
Length of cloth required for one shirt = 2 m 15 cm = 2 x 100 + 15 = 215 cm
Number of shirts that can be stitched = Total length of cloth / Length of cloth required for one shirt
Number of shirts = 4000 / 215 = 18 shirts
Remaining cloth = Total length of cloth – (Number of shirts x Length of cloth required for one shirt)
Remaining cloth = 4000 – (18 x 215)
Remaining cloth = 4000 – 3870
Remaining cloth = 130 cm
Therefore, 18 shirts can be stitched out of 40 m, and 1 m 30 cm of cloth is left.
10. Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?
Sol.
Weight of one box in g = (4 x 1000) + 500 = 4500 g
Maximum weight the van can carry in g = 800 x 1000 = 800,000 g
Number of boxes that can be loaded in the van = Maximum weight the van can carry / Weight of one box
Number of boxes = 800,000 / 4500 = 177 boxes
Therefore, 177 boxes can be loaded in the van.
11. The distance between the school and a student’s house is 1 km 875 m. Every day, she walks both ways. Find the total distance covered by her in six days.
Sol.
Total distance covered in one trip = Distance to school + Distance to house
Total distance covered in one trip = 1 km 875 m + 1 km 875 m = 3 km 750 m
Total distance covered in six days = Total distance covered in one day x Number of trips in six days
Total distance covered = 3 km 750 m x 6
Total distance covered = 22 km 500 m
Therefore, the total distance covered by the student in six days is 22 km 500 m.
12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
Sol.
Total quantity of curd in ml = (4 x 1000) + 500 = 4500 ml
Capacity of one glass = 25 ml
Number of glasses that can be filled = Total quantity of curd / Capacity of one glass
Number of glasses = 4500 / 25 = 180 glasses
Therefore, 180 glasses can be filled with curd.
NCERT Solutions for Class 6 Chapter 1 Knowing Our Numbers Exercise 1.3
NCERT solutions for class 6 Maths exercise 1.3 focuses on practicing the concept of comparing and ordering numbers. This exercise helps students understand the relative values of different numbers and enhances their ability to arrange numbers in ascending or descending order.
1. Estimate each of the following using the general rule:
(a) 730 + 998
(b) 796 – 314
(c) 12904 + 2888
(d) 28292 – 21496
Sol.
(a) 730 + 998
Rounded to nearest hundreds:
730 is about 700
998 is about 1000
Estimated sum is about 700 + 1000 = 1700
(b) 796 – 314
Rounded to nearest hundreds:
796 is about 800
314 is about 300
Estimated difference is about 800 – 300 = 500
(c) 12904 + 2888
Rounded to nearest thousands:
12904 is about 13000
2888 is about 3000
Estimated sum is about 13000 + 3000 = 16000
(d) 28292 – 21496
Rounded to nearest thousands:
28292 is about 28000
21496 is about 21000
Estimated difference is about 28000 – 21000 = 7000
2. Give a rough estimate (by rounding off to the nearest hundreds) and also a closer estimate (by rounding off to the nearest tens):
(a) 439 + 334 + 4317
(b) 108734 – 47599
(c) 8325 – 491
(d) 489348 – 48365
Sol.
(a) 439 + 334 + 4317
Rounded to nearest hundreds:
439 is about 400
334 is about 300
4317 is about 4300
Estimated sum is about 400 + 300 + 4300 = 5000
Rounded to nearest tens:
439 is about 440
334 is about 330
4317 is about 4320
Estimated sum is about 440 + 330 + 4320 = 5090
(b) 108734 – 47599
Rounded to nearest hundreds:
108734 is about 108700
47599 is about 47600
Estimated difference is about 108700 – 47600 = 61100
Rounded to nearest tens:
108734 is about 108730
47599 is about 47600
Estimated difference is about 108730 – 47600 = 61130
(c) 8325 – 491
Rounded to nearest hundreds:
8325 is about 8300
491 is about 500
Estimated difference is about 8300 – 500 = 7800
Rounded to nearest tens:
8325 is about 8330
491 is about 490
Estimated difference is about 8330 – 490 = 7840
(d) 489348 – 48365
Rounded to nearest hundreds:
489348 is about 489300
48365 is about 48400
Estimated difference is about 489300 – 48400 = 440900
Rounded to nearest tens:
489348 is about 489350
48365 is about 48370
Estimated difference is about 489350 – 48370 = 440980
3. Estimate the following products using the general rule:
(a) 578 × 161
(b) 5281 × 3491
(c) 1291 × 592
(d) 9250 × 29
Sol.
(a) 578 × 161
Rounded to nearest hundreds:
578 is about 600
161 is about 200
Estimated product is about 600 × 200 = 120000
(b) 5281 × 3491
Rounded to nearest thousands:
5281 is about 5000
3491 is about 3500
Estimated product is about 5000 × 3500 = 17500000
(c) 1291 × 592
Rounded to nearest hundreds:
1291 is about 1300
592 is about 600
Estimated product is about 1300 × 600 = 780000
(d) 9250 × 29
Rounded to nearest hundreds:
9250 is about 9000
29 is about 30
Estimated product is about 9000 × 30 = 270000
- Chapter 1 Knowing Our Numbers
- Chapter 2 Whole Numbers
- Chapter 3 Playing With Numbers
- Chapter 4 Basic Geometrical Ideas
- Chapter 5 Understanding Elementary Shapes
- Chapter 6 Integers
- Chapter 7 Fractions
- Chapter 8 Decimals
- Chapter 9 Data Handling
- Chapter 10 Mensuration
- Chapter 11 Algebra
- Chapter 12 Ratio and Proportion
- Chapter 13 Symmetry
- Chapter 14 Practical Geometry
NCERT Class 6 Maths Chapter 1 Solutions Summary
NCERT Class 6 Maths Chapter 1 “Knowing Our Numbers” covers various fundamental concepts related to numbers. The chapter includes topics such as comparing numbers, ascending and descending order, place value, larger numbers, estimation, and the use of commas. Students will learn about shifting digits, estimating sums and products, BODMAS, and using brackets. The chapter aims to strengthen basic mathematical concepts, enhance problem-solving skills, and prepare students for exams. NCERT Solutions for Chapter 1 provide detailed explanations, examples, and exercises to help students understand and apply these concepts effectively. The solutions are designed by subject experts to align with CBSE guidelines and NCERT marking schemes, ensuring comprehensive preparation for students. By practicing the exercises in the chapter, students can gain a solid foundation in mathematical principles and excel in their studies.
| Other Resources for Class 6 | |
| Worksheet for Class 6 All subjects | CBSE Notes Class 6 |
| NCERT Books for Class 6 | Online Tuition for Class 6 |
FAQs on NCERT Solutions for Class 6 Maths Chapter 1 Knowing Our Numbers
What are the benefits of NCERT Solutions for Class 6 Maths Chapter 1 for CBSE exams?
NCERT Solutions for Class 6 Maths Chapter 1 are great for CBSE exams because they explain concepts clearly. They help students understand numbers better, which is key for exams.
What is interesting in knowing our numbers?
Knowing Our Numbers is interesting because it shows us how to handle big numbers, compare them, and use them in our daily life.
What is the first chapter of Class 6 Maths Solutions?
The first chapter of Class 6 Maths Solutions is Knowing Our Numbers. It's about understanding and working with different sizes of numbers.
What are the objectives of knowing our numbers Class 6?
The objectives of Knowing Our Numbers Class 6 are to learn about large numbers, their comparison, and their use in various scenarios.
Where to Download NCERT Solutions for Class 6 Maths?
You can download NCERT Solutions for Class 6 Maths from Infinity Learn. They offer complete chapter-wise solutions with explanations.
