Wednesday, May 29, 2024

Knowing Our Numbers

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NCERT Solutions for Class 6 Maths Chapter 1

Chapter 1: Knowing Our Numbers from your 6th-grade math book explores these concepts:

The Number System:

  • Natural Numbers: Numbers used for counting objects, starting from 1 and going on infinitely (1, 2, 3, 4, …).
  • Whole Numbers: Natural numbers including 0. So, whole numbers are 0, 1, 2, 3, and so on.
  • Place Value System: This concept explains the value of each digit in a number based on its position. You’ll likely revisit units, tens, hundreds, thousands, and so on. For example, in 3456, the digit 3 is in the thousands place and has a value of 3 * 1000 (3000), the 4 is in the hundreds place with a value of 4 * 100 (400), and so on.

Comparing Numbers:

  • Techniques to compare numbers will be introduced. Here are two common methods:
    • Number of Digits: If two numbers have a different number of digits, the one with more digits is generally bigger. (For example, 256 is greater than 18).
    • Place Value Comparison: If numbers have the same number of digits, you compare them digit by digit, starting from the leftmost place (highest value). The number with the greater digit in the leftmost differing place is considered bigger. (For example, 4872 is greater than 4789 because 8 in the thousands place of 4872 is greater than 7 in the thousands place of 4789).

Ordering Numbers:

  • You’ll learn how to arrange numbers in a specific order:
    • Ascending Order: Arranging numbers from smallest to biggest (e.g., 12, 15, 20).
    • Descending Order: Arranging numbers from biggest to smallest (e.g., 20, 15, 12).

NCERT Solutions for Class 6 Maths Chapter 1

Exercise 1.1 

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.

Ans : 

(a) 1 lakh = 10 ten thousand. 

(b) 1 million = 10 hundred thousand. 

(c) 1 crore = 10 ten lakh. 

(d) 1 crore = 10 million.

(e) 1 million = 10 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.

Ans : 

(a) 73,75,307 

(b) 9,05,00,041 

(c) 7,52,21,302 

(d) 58,423,202 

(e) 23,30,010

3. Insert commas suitably and write the names according to Indian System of Numeration:

(a) 87595762

(b) 8546283

(c) 99900046

(d) 98432701

Ans : 

a) 8,75,95,762 (Eight crore seventy-five lakh ninety-five thousand seven hundred and sixty-two)

 (b) 85,46,283 (Eighty-five lakh forty-six thousand two hundred and eighty-three) 

(c) 9,99,00,046 (Nine crore ninety-nine lakh and forty-six) 

(d) 9,84,32,701 (Nine crore eighty-four lakh thirty-two thousand seven hundred and one)

4. Insert commas suitably and write the names according to International System of Numeration:

(a) 78921092

(b) 7452283

(c) 99985102

(d) 48049831

Ans : 

(a) 78,921,092 (Seventy-eight million nine hundred twenty-one thousand and ninety-two)

(b) 7,452,283 (Seven million four hundred fifty-two thousand two hundred eighty-three) 

(c) 99,985,102 (Ninety-nine million nine hundred eighty-five thousand one hundred and two) 

(d) 48,049,831 (Forty-eight million forty-nine thousand eight hundred thirty-one)

Exercise 1.2 

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 the four days.

Ans : 

DayNumber of Tickets Sold
Day 11094
Day 21812
Day 32050
Day 42751

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?

Ans : In order to complete 10,000 runs, Shekhar needs to score 3020 more runs.

10000(The runs he Wish)-6980 (Runs he scored)= 3020

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?

Ans : 

CandidateVotes Received
Successful Candidate577,500
Nearest Rival348,700
Margin of Victory228,800

Successful Candidate – Nearest Rival = Margin Of Victory

4. Kirti bookstore sold books worth ₹2,85,891 in the first week of June and books worth ₹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?

Ans : 

Week 1₹ 2,85,891
Week 2₹ 4,00,768
Total₹ 6,86,659

Book Sold in 2nd Month – Book sold in 1st Month 

= ₹4,00,768 – ₹2,85,891 = ₹1,14,877

The total sale for the two weeks is ₹ 686,659 and Week 2 had higher sales by ₹ 114,877.

5. Find the difference between the greatest and the least numbers that can be written using the digits 6, 2, 7, 4, 3 each only once.

Ans : 

  1. Greatest Number: Arrange the digits in descending order (from largest to smallest). This gives us: 76432.
  2. Least Number: Arrange the digits in ascending order (from smallest to largest). This gives us: 23467.
  3. Difference: Now, subtract the least number from the greatest number.

Difference = Greatest Number – Least Number Difference = 76432 – 23467

Difference = 52965

6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January, 2006?

Ans : The machine produced 87,575 screws in the month of January, 2006.

January 2006 has 31 days. Since the machine manufactures 2,825 screws a day, to find the total number of screws produced in the entire month, we can multiply the daily production by the number of days:

Number of screws produced = Daily production * Number of days in January

= 2,825 screws/day * 31 days = 87,575 screws

Therefore, the machine produced a total of 87,575 screws in January 2006.

7. A merchant had ₹78,592 with her. She placed an order for purchasing 40 radio sets at ₹1200 each. How much money will remain with her after the purchase?

Ans : 

  1. Total cost of radio sets: Number of radio sets * Cost per radio set = Total cost 40 radio sets * ₹1200/radio set = ₹48,000
  2. Money remaining: Money with merchant – Total cost of radio sets = Remaining money ₹78,592 – ₹48,000 = ₹30,592

Therefore, the merchant will have ₹30,592 remaining after the purchase.

8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?

Ans : 

  1. Calculate the difference between the two multipliers: 65 – 56 = 9
  2. Multiply this difference (9) by the original number (7236) to find the difference in the product: 7236 * 9 = 65,124

Therefore, the student’s answer was 65,124 more than the correct answer.

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?

Ans : 

Total length of the cloth = 40 m = 40 x 100 cm = 4000 cm.

Cloth needed to stitch a shirt = 2 m 15 cm = 2 x 100 + 15 cm = 215 cm

Therefore, number of shirts stitched = 4000/215

The number of shirts stitched = 18 and the remaining cloth = 130 cm 

10 . Medicine is packed in boxes, each weighing 4 kg 500 g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?

Ans : 

  1. Convert weight of a box to kg: There are 1000 grams (g) in 1 kilogram (kg). So, 4 kg 500 g is equal to 4 kg + (500 g / 1000 g/kg) = 4.5 kg.
  2. Calculate how many boxes the van can hold: Divide the van’s maximum weight capacity (800 kg) by the weight of a box (4.5 kg). Since you can’t load parts of boxes, round down the result to get the whole number of boxes: Number of boxes = Floor(800 kg / 4.5 kg/box) ≈ 177 boxes.
    Therefore, the van can carry approximately 177 boxes.

11. The distance between the school and the house of a student is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.

Ans : 

The student walks 1.875 km each way (to school and back), so for a round trip that’s 1.875 km * 2 = 3.75 km each day.

Since there are six days, the total distance covered in six days is 3.75 km/day * 6 days = 22.5 km.

12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 mL capacity, can it be filled? 

Ans : There are 4500 milliliters of curd in the vessel because 4 liters is equal to 4 * 1000 milliliters = 4000 milliliters, and there are another 500 milliliters.

We can fill 180 glasses because 4500 milliliters / 25 milliliters/glass = 180 glasses.

So the answer is 180

NCERT Solutions for Class 6 Maths Chapter 1


What concepts are covered in NCERT Solutions for Class 6 Maths Chapter 1, “Knowing Our Numbers”?

NCERT Solutions for Class 6 Maths Chapter 1 delve into essential numerical concepts such as place value, comparing numbers, rounding off, estimation, and properties of numbers.

How do NCERT Solutions for Class 6 Maths Chapter 1 help in understanding “Knowing Our Numbers”?

NCERT Solutions provide comprehensive explanations and practice exercises that aid in grasping the fundamentals of numbers, facilitating better comprehension and application of mathematical concepts.

Can Class 6 Maths Chapter 1 knowing our numbers assist in improving numerical skills and problem-solving abilities?

Yes, Class 6 Maths Chapter knowing our numbers offers a structured approach to learning numbers, fostering numerical fluency, critical thinking, and problem-solving skills through engaging exercises and real-life scenarios.

What are some key topics explored under “Knowing Our Numbers,” as discussed in Class 6 Maths Chapter 1 ?

Class 6 Maths Chapter 1 knowing our numbers covers a range of topics, including place value system, comparison of numbers, rounding off, estimation, and the significance of numbers in various contexts, laying a strong foundation in arithmetic.

How can students benefit from practicing NCERT Solutions for Class 6 Maths Chapter 1?

By practicing NCERT Solutions for Class 6 Maths Chapter knowing our numbers , students can enhance their numerical proficiency, gain confidence in handling mathematical problems, and develop a deeper understanding of the principles underlying numbers and their applications.

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