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## NCERT Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers Ex 1.1

**Exercise 1.1**

**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**:

**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

**Question 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.**

**Solution**:

The solution is as follows,

**a** 73,75,307

**b** 9,05,00,041

**c** 7,52, 21,302

**d** 58, 423, 202

**e** 23,30,010

**Question 3:**

**Insert commas suitable and write the names according to Indian system of**

**numeration:**

**(a) 87595762 **

**(b) 8546283**

**(c) 99900046**

**(d) 98432701**

**Solution**:

The Indian system of numeration is crores, lakhs, thousands, hundreds, tens and ones. The solution is as follows:

**a** 8,75,95,762

Eight crore seventy-five lakh ninety-five thousand seven hundred sixty two

**b** 85,46,283

Eighty five lakh forty six thousand two hundred eighty three

**c** 9,99,00,046

Nine crore ninety nine lakh forty six

**d** 9,84,32,701

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:**

**(a) 78921092**

**(b) 7452283**

**(c) 99985102**

**(d) 48049831**

**Solution**:

In the International System of Numeration, we have ones, tens, hundreds, thousands and then

millions.

**a** 78,921,092

Seventy eight million nine hundred twenty one thousand 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 two

**d** 48,049,831

Forty eight million forty nine thousand eight hundred thirty one.

## NCERT Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers Ex 1.2

**Exercise 1.2**

**Question 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.**

**Solution**:

Calculate the total number of tickets sold on all the four days:

Hence, the total number of tickets sold are 7707 .

**Question 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?**

**Solution**:

Until now Shekhar has scored 6980 runs and if he wishes to score 10000 runs then

3020 runs are required to complete 10000 runs.

**Question 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?**

**Solution**:

The winner registered 5,77,500 votes and the other candidate got 3,48,700 votes, so to calculate the margin,

2,28,800 is the margin by which the winner won the election.

**Question 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?**

**Solution**:

The total sale can be calculated by adding the sale of both the weeks,

Sale for the first week 2,85,891

Sale for the second week 4,00,768

It can be seen from the question that the sales in the second week were greater than that in the

first week, so,

The sales in the second week were more and by

Rs. 1,14,877 .

**Question 5:**

**Find the difference between the greatest and the least number that can be**

**written using the digits 6, 2, 7, 4, 3 each only once.**

**Solution**:

The largest 5 digit number using the given digits is

76432 .

The smallest 5 digit number using the given digits is

23467 .

The difference is calculated as,

The difference between the largest and the smallest number formed with the digits 6, 2, 7, 4, 3 is 52,965 .

**Question 6:**

**A machine, on an average, manufactures 2,825 screws a day. How many**

**screws did it produce in the month of January 2006?**

**Solution**:

The number of days in the month of January is 31 and the machine produces 2,825 screws in a day on an average, so the total number of screws produced is,

87,575 screws were produced in January 2006 .

**Question 7:**

**A merchant had ₹ 78,592 with her. She placed an order for purchasing 40**

**radio sets at ₹ 1,200 each. How much money will remain with her after the**

**purchase?**

**Solution**:

A radio costs Rs. 1200 and she placed an order for 40 sets, so,

The merchant has spent Rs. 48,000 in buying the radios, the money left with her is,

Hence, the money left with her is Rs. 30,592 .

**Question 8:**

**A student multiplied 7236 by 65 instead of multiplying by 56. By how much**

**was his answer greater than the correct answer?**

**Solution**:

The answer after multiplying 7236 by 65

is,

The actual answer 7236 multiplying by 56

is,

Thus, the difference is,

The difference between the wrong answer and right answer is

65124 .

**Question 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?**

**Solution**:

First we will convert the units into a common unit, we are converting meter into centimeters.

1 m =100 cm

40 m =4000 cm

Cloth required for 1 shirt = 2 m 15 cm.

Cloth required for 1 shirt = 215 cm.

Now, number of shirts that can be stitched is 4000 ÷ 215

So, 18 shirts can be stitched from the given cloth and 130 cm of cloth will be left out.

**Question 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?**

**Solution**:

We will convert the given data in a particular unit,

1 kg =1000 grams

4 kg =4000 grams

4 kg 500 grams= 4500 grams

800 kg =800000 grams

Now, we know a box weighs 4500 grams so number of boxes that can come in a van that can hold only 800000 grams, 800000 ÷ 4500,

So, 177 boxes can be loaded in the van.

**Question 11:**

**The distance between the school and the house of 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.**

**Solution**:

We will convert the given data in a particular unit,

1 km =1000 m

1 km 875 m =1875 m

Now, the girl daily goes to school and comes back from the school so the total distance covered by the girl in a day,

The distance covered in a day by the girl is 3750 m. Now calculating the distance travelled by the girl in 6 days,

The distance travelled by the girl in 6 days is 22500 m.

**Question 12:**

**A vessel has 4 liters and 500 ml of curd. In how many glasses each of 25 ml**

**capacity, can it be filled?**

**Solution**:

We will convert the given data in a particular unit,

1 liter= 1000 ml

4 liters= 4000 ml

4 liters 500 ml=4500 ml

The capacity of glasses is 25 ml, so the number of glasses is,

180 glasses of 25 ml can be filled.

## NCERT Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers Ex 1.3

**Question 1:**

**Estimate each of the following using general rule:**

**(a) 730 + 998**

**(b) 796 – 314**

**(c) 12,904 + 2,888**

**(d) 28,292 – 21,496**

**Solution:**

(a) 730 is round off to 700 and 998 is round off to 1000 and the estimated sum is 1700

(b) 796 is round off to 800 and 314 is round off to 300 and the estimated difference is 500

(c) 12,904 is round off to 13000 and 2,888 is round off to 3000 and the estimated sum is 16000

(d) 28,292 is round off to 28,000 and 21,496 is round off to 21,000 and the estimated difference is 7,000.

**Question 2:**

**Give a rough estimate (by rounding off to nearest hundreds) and also a**

**closer estimate (by rounding off to nearest tens):**

**(a) 439 + 334 + 4317**

**(b) 1, 08,734 – 47,599**

**(c) 8325 – 491**

**(d) 4, 89,348 – 48,365**

**Solution**:

(a) 439 is round off to 400; 334 is round off to 300 and 4317 is round off to 4300, so the estimated sum is 5000 (rounding off to nearest hundreds)

439 is round off to 440; 334 is round off to 330 and 4317 is round off to 4320, so the estimated sum is 5090 (rounding off to nearest tens).

(b) 108734 is round off to 108700 (for hundreds) and 108730 (for tens) and 47599 is round off to 47600 (for hundreds and tens), so the estimated difference is 61100 (for hundreds) and 61130 (for tens).

(c) 8325 is round off to 8300 (for hundreds) and 8330 (for tens) and 491 is round off to 500 (for hundreds) and 490 (for tens), so the estimated difference is 7800 and 7840.

(d) 489348 is round off to 489300 (for hundreds) and 489350 (for tens) and 48365 is round off to 48400 (for hundreds) and 48370 (for tens), so the estimated difference is 440900 (for hundreds) and 440980 (for tens).

**Question 3:**

**Estimate the following products using general rule:**

**(a) 578 x 161**

**(b) 5281 x 3491**

**(c) 1291 x 592**

**(d) 9250 x 29**

**Solution**:

(a) 578 is round off to 600 and 161 is round off to 200 and the estimated product is 120000.

(b) 5281 is round off to 5000 and 3491 is round off to 3500 and the estimated product is 17500000.

(c) 1291 is round off to 1300 and 592 is round off to 600 and the estimated product is 780000.

(d) 9250 is round off to 9000 and 29 is round off to 30 and the estimated product is 270000.