Class – 6 CH-1 KNOWING OUR NUMBERS

MATHS NCERT SOLUTIONS

EXERCISE 1.1

Question 1:

Fill in the blanks:

(a) 1 lakh = _______________ ten thousand

(b) 1 million = _______________ hundred thousand

(d) 1 crore = _______________ million

(e) 1 million = _______________ lakh

SOLUTION 1:

(a) 10

(b) 10

(d) 10

(e) 10

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.

(d) Fifty-eight million four hundred twenty-three thousand two hundred two.

(e) Twenty-three lakh thirty thousand ten.

SOLUTION 2:

(a) 73,75,307

(b) 9,05,00,041

(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

(d) 98432701

SOLUTION 3:

(a) 8,75,95,762

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

(b) 85,46,283

Eight-five lakh forty-six thousand two hundred eighty-three.

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

(d) 48049831

SOLUTION 4:

(a) 78,921,092

Seventy-eight million nine hundred twenty-one thousand ninety-two

(b) 7,452,483

Seven million four hundred fifty-two thousand two hundred eighty-three

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

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 1:

Number of tickets sold on first day = 1,094

Number of tickets sold on second day = 1,812

Number of tickets sold on third day = 2,050

Number of tickets sold on fourth day = + 2,751

Total tickets sold = 7,707

Therefore, 7,707 tickets were sold on all the four days.

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 2:

Runs to achieve = 10,000

Runs scored = – 6,980

Runs required = 3,020

Therefore, he needs 3,020 more 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 3:

Number of votes secured by successful candidates = 5,77,500

Number of votes secured by his nearest rival = – 3,48,700

Margin between them = 2,28,800

Therefore, the successful candidate won by a margin of 2,28,800 votes.

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 4:

Books sold in first week = 2,85,891

Books sold in second week = + 4,00,768

Total books sold = 6,86,659

Since, 4,00,768,> 2,85,891

Therefore sale of second week is greater than that of first week.

Books sold in second week = 4,00,768

Books sold in first week = – 2,85,891

More books sold in second week = 1,14,877

Therefore, 1,14,877 more books were sold in second week.

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 5:

Greatest five-digit number using digits 6,2,7,4,3 = 76432

Smallest five-digit number using digits 6,2,7,4,3 = – 23467

Difference = 52965

Therefore the difference is 52965.

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 6:

Number of screws manufactured in one day = 2,825

Number of days in the month of January (31 days) = 2,825 x 31 = 87,575

Therefore, the machine produced 87,575 screws in the month of January.

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 7:

Cost of one radio = ₹ 1200

Cost of 40 radios = 1200 x 40

Now, = ₹ 48,000

Total money with merchant = ₹ 78,592

Money spent by her = – ₹ 48,000

Money left with her = ₹ 30,592

Therefore, ₹ 30,592 will remain with her after the purchase.

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 8:

Wrong answer = 7236 x 65 = 470340

Correct answer = 7236 x 56 =405216

Difference in answers = 470340 – 405216 = 65,124

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 9:

Cloth required to stitch one shirt = 2 m 15 cm

= 2 x 100 cm + 15 cm

= 215 cm

Length of cloth = 40 m = 40 x 100 cm = 4000 cm

Number of shirts can be stitched = 4000 ÷ 215

Therefore, 18 shirts can be stitched and 130 cm (1 m 30 cm) cloth will remain.

Question 10:

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

SOLUTION 10:

The weight of one box = 4 kg 500 g = 4 x 1000 g + 500 g = 4500 g

Maximum load can be loaded in van = 800 kg = 800 x 1000 g = 800000 g

Number of boxes = 800000 ÷ 4500

Therefore, 177 boxes can be loaded.

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 11:

Distance between school and home = 1.875 km

Distance between home and school = + 1.875 km

Total distance covered in one day = 3.750 km

Distance covered in six days = 3.750 x 6 = 22.500 km

Therefore, 22 km 500 m distance covered in six days.

Question 12:

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

SOLUTION 12:

Capacity of curd in a vessel = 4 litres 500 ml = 4 x 1000 ml + 500 ml = 4500 ml

Capacity of one glass = 25 ml

Number of glasses can be filled = 4500 ÷ 25

Therefore, 180 glasses can be filled by curd.

Exercise 1.3

Question 1:

Estimate each of the following using general rule:

(a) 730 + 998

(b) 796 – 314

(d) 28,292 – 21,496

SOLUTION 1:

(a) 730 round off to 700

998 round off to 1000

Estimated sum = 1700

(b) 796 round off to 800

314 round off to 300

Estimated sum = 500

2888 round off to 3000

Estimated sum = 16000

(d) 28292 round off to 28000

21496 round off to 21000

Estimated difference = 7000

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) 1,08,737 – 47,599

(d) 4,89,348 – 48,365

SOLUTION 2:

(a) 439 round off to 400

334 round off to 300

4317 round off to 4300

Estimated sum = 5000

(b) 108734 round off to 108700

47599 round off to 47600

Estimated difference = 61100

491 round off to 500

Estimated difference = 7800

(d) 489348 round off to 489300

48365 round off to 48400

Estimated difference = 440900

Question 3:

Estimate the following products using general rule:

(a) 578 x 161

(b) 5281 x 3491

(d) 9250 x 29

SOLUTION 3:

(a) 578 x 161

578 round off to 600

161 round off to 200

The estimated product = 600 x 200 = 1,20,000

(b) 5281 x 3491

5281 round of to 5,000

3491 round off to 3,500

The estimated product = 5,000 x 3,500 = 1,75,00,000

1291 round off to 1300

592 round off to 600

The estimated product = 1300 x 600 = 7,80,000

(d) 9250 x 29

9250 round off to 10,000

229 round off to 30

The estimated product = 10,000 x 30 = 3,00,000

Sunday, December 17, 2023