Solutions
NCERT Class 6 Maths Solutions for Chapter 1 Knowing Our Numbers
Exercise 1.1 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.
(a) 1 lakh = ………….. ten thousand.
(b) 1 million = ………… hundred thousand.
(c) 1 crore = ………… ten lakhs.
(d) 1 crore = ………… million.
(e) 1 million = ………… lakhs.
Solutions:
(a) 1 lakh = 10 ten thousand
(b) 1 million = 10 hundred thousand
(c) 1 crore = 10 ten lakhs
(d) 1 crore = 10 million
(e) 1 million = 10 lakhs
(a) 1 lakh = 10 ten thousand
(b) 1 million = 10 hundred thousand
(c) 1 crore = 10 ten lakhs
(d) 1 crore = 10 million
(e) 1 million = 10 lakhs
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
(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
Solutions:
(a) 73,75,307
(b) 9,05,00,041
(c) 7,52,21,302
(d) 5,84,23,202
(e) 23,30,010
(a) 73,75,307
(b) 9,05,00,041
(c) 7,52,21,302
(d) 5,84,23,202
(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
(a) 87595762 (b) 8546283 (c) 99900046 (d) 98432701
Solutions:
(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
(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
4. Insert commas suitably and write the names according to the International System of Numeration:
(a) 78921092 (b) 7452283 (c) 99985102 (d) 48049831
(a) 78921092 (b) 7452283 (c) 99985102 (d) 48049831
Solutions:
(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
(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
Exercise 1.2 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.
Solutions:
Number of tickets sold on 1st day = 1094
Number of tickets sold on 2nd day = 1812
Number of tickets sold on 3rd day = 2050
Number of tickets sold on 4th day = 2751
Hence, the total number of tickets sold on all four days = 1094 + 1812 + 2050 + 2751 = 7707 tickets
Number of tickets sold on 1st day = 1094
Number of tickets sold on 2nd day = 1812
Number of tickets sold on 3rd day = 2050
Number of tickets sold on 4th day = 2751
Hence, the total number of tickets sold on all four days = 1094 + 1812 + 2050 + 2751 = 7707 tickets
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?
Solutions:
Shekhar scored = 6980 runs
He wants to complete = 10000 runs
Runs needed to score more = 10000 – 6980 = 3020
Hence, he needs 3020 more runs to score
Shekhar scored = 6980 runs
He wants to complete = 10000 runs
Runs needed to score more = 10000 – 6980 = 3020
Hence, he needs 3020 more runs to score
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?
Solutions:
No. of votes secured by the successful candidate = 577500
No. of votes secured by his rival = 348700
Margin by which he won the election = 577500 – 348700 = 228800 votes
∴ The successful candidate won the election by 228800 votes
No. of votes secured by the successful candidate = 577500
No. of votes secured by his rival = 348700
Margin by which he won the election = 577500 – 348700 = 228800 votes
∴ The successful candidate won the election by 228800 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?
Solutions:
Price of books sold in the first week of June = Rs 285891
Price of books sold in the second week of June = Rs 400768
No. of books sold in both weeks together = Rs 285891 + Rs 400768 = Rs 686659
The sale of books is the highest in the second week.
Difference in the sale in both weeks = Rs 400768 – Rs 285891 = Rs 114877
∴ Sale in the second week was greater by Rs 114877 than in the first week.
Price of books sold in the first week of June = Rs 285891
Price of books sold in the second week of June = Rs 400768
No. of books sold in both weeks together = Rs 285891 + Rs 400768 = Rs 686659
The sale of books is the highest in the second week.
Difference in the sale in both weeks = Rs 400768 – Rs 285891 = Rs 114877
∴ Sale in the second week was greater by Rs 114877 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.
Solutions:
Digits given are 6, 2, 7, 4, 3
Greatest 5-digit number = 76432
Least 5-digit number = 23467
Difference between the two numbers = 76432 – 23467 = 52965
∴ The difference between the two numbers is 52965.
Digits given are 6, 2, 7, 4, 3
Greatest 5-digit number = 76432
Least 5-digit number = 23467
Difference between the two numbers = 76432 – 23467 = 52965
∴ The difference between the two numbers is 52965.
6. A machine, on average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
Solutions:
Number of screws manufactured in a day = 2825
Since January month has 31 days,
The number of screws manufactured in January = 31 × 2825 = 87575
Hence, the machine produced 87575 screws in the month of January 2006.
Number of screws manufactured in a day = 2825
Since January month has 31 days,
The number of screws manufactured in January = 31 × 2825 = 87575
Hence, the machine produced 87575 screws in the month of 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?
Solutions:
Total money the merchant had = Rs 78592
The number of radio sets she placed an order for purchasing = 40 radio sets
Cost of 1 radio set = Rs 1200
Total cost of 40 radio sets = 1200 × 40 = 48000
Remaining money = Rs 78592 – Rs 48000 = Rs 30592
∴ After purchasing, the merchant will have Rs 30592.
Total money the merchant had = Rs 78592
The number of radio sets she placed an order for purchasing = 40 radio sets
Cost of 1 radio set = Rs 1200
Total cost of 40 radio sets = 1200 × 40 = 48000
Remaining money = Rs 78592 – Rs 48000 = Rs 30592
∴ After purchasing, the merchant will have Rs 30592.
8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?
Solutions:
Difference between 65 and 56 = 65 – 56 = 9
So, the student’s answer was greater by 7236 × 9 = 65124
Hence, the student’s answer was greater than the correct answer by 65124.
Difference between 65 and 56 = 65 – 56 = 9
So, the student’s answer was greater by 7236 × 9 = 65124
Hence, the student’s answer was greater than the correct answer by 65124.
9. To stitch a shirt, 2 m 15 cm of cloth is needed. Out of 40 m of cloth, how many shirts can be stitched and how much cloth will remain?
Solutions:
Total cloth = 40 m = 4000 cm
Cloth required for one shirt = 2 m 15 cm = 215 cm
Number of shirts that can be made out of 4000 cm cloth = 4000 ÷ 215 = 18 shirts
Remaining cloth = 4000 – (215 × 18) = 4000 – 3870 = 130 cm = 1 m 30 cm
∴ 18 shirts can be made and 1 m 30 cm cloth will remain.
Total cloth = 40 m = 4000 cm
Cloth required for one shirt = 2 m 15 cm = 215 cm
Number of shirts that can be made out of 4000 cm cloth = 4000 ÷ 215 = 18 shirts
Remaining cloth = 4000 – (215 × 18) = 4000 – 3870 = 130 cm = 1 m 30 cm
∴ 18 shirts can be made and 1 m 30 cm cloth will remain.
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?
Solutions:
Total weight the van can carry = 800 kg
Weight of 1 box = 4 kg 500 g = 4.5 kg
Number of boxes the van can carry = 800 ÷ 4.5 = 177 boxes
∴ The van can carry 177 boxes of medicines.
Total weight the van can carry = 800 kg
Weight of 1 box = 4 kg 500 g = 4.5 kg
Number of boxes the van can carry = 800 ÷ 4.5 = 177 boxes
∴ The van can carry 177 boxes of medicines.
Exercise 1.3 Page No: 23
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
(a) 730 + 998
(b) 796 – 314
(c) 12,904 + 2,888
(d) 28,292 – 21,496
Solutions:
(a) 730 + 998
Rounding off to hundreds:
730 rounds off to 700,
998 rounds off to 1000.
So, 700 + 1000 = 1700
(b) 796 – 314
Rounding off to hundreds:
796 rounds off to 800,
314 rounds off to 300.
So, 800 – 300 = 500
(c) 12,904 + 2,888
Rounding off to thousands:
12904 rounds off to 13000,
2888 rounds off to 3000.
So, 13000 + 3000 = 16000
(d) 28,292 – 21,496
Rounding off to thousands:
28292 rounds off to 28000,
21496 rounds off to 21000.
So, 28000 – 21000 = 7000
(a) 730 + 998
Rounding off to hundreds:
730 rounds off to 700,
998 rounds off to 1000.
So, 700 + 1000 = 1700
(b) 796 – 314
Rounding off to hundreds:
796 rounds off to 800,
314 rounds off to 300.
So, 800 – 300 = 500
(c) 12,904 + 2,888
Rounding off to thousands:
12904 rounds off to 13000,
2888 rounds off to 3000.
So, 13000 + 3000 = 16000
(d) 28,292 – 21,496
Rounding off to thousands:
28292 rounds off to 28000,
21496 rounds off to 21000.
So, 28000 – 21000 = 7000
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 + 4,317
(b) 1,08,734 – 47,599
(c) 8325 – 491
(d) 4,89,348 – 48,365
(a) 439 + 334 + 4,317
(b) 1,08,734 – 47,599
(c) 8325 – 491
(d) 4,89,348 – 48,365
Solutions:
(a) 439 + 334 + 4317
Rounding off to nearest hundreds:
439 rounds off to 400,
334 rounds off to 300,
4317 rounds off to 4300.
So, 400 + 300 + 4300 = 5000
Rounding off to nearest tens:
439 rounds off to 440,
334 rounds off to 330,
4317 rounds off to 4320.
So, 440 + 330 + 4320 = 5090
(b) 1,08,734 – 47,599
Rounding off to nearest hundreds:
1,08,734 rounds off to 1,08,700,
47,599 rounds off to 47,600.
So, 1,08,700 – 47,600 = 61,100
Rounding off to nearest tens:
1,08,734 rounds off to 1,08,730,
47,599 rounds off to 47,600.
So, 1,08,730 – 47,600 = 61,130
(c) 8325 – 491
Rounding off to nearest hundreds:
8325 rounds off to 8300,
491 rounds off to 500.
So, 8300 – 500 = 7800
Rounding off to nearest tens:
8325 rounds off to 8330,
491 rounds off to 490.
So, 8330 – 490 = 7840
(d) 4,89,348 – 48,365
Rounding off to nearest hundreds:
4,89,348 rounds off to 4,89,300,
48,365 rounds off to 48,400.
So, 4,89,300 – 48,400 = 4,40,900
Rounding off to nearest tens:
4,89,348 rounds off to 4,89,350,
48,365 rounds off to 48,370.
So, 4,89,350 – 48,370 = 4,40,980
(a) 439 + 334 + 4317
Rounding off to nearest hundreds:
439 rounds off to 400,
334 rounds off to 300,
4317 rounds off to 4300.
So, 400 + 300 + 4300 = 5000
Rounding off to nearest tens:
439 rounds off to 440,
334 rounds off to 330,
4317 rounds off to 4320.
So, 440 + 330 + 4320 = 5090
(b) 1,08,734 – 47,599
Rounding off to nearest hundreds:
1,08,734 rounds off to 1,08,700,
47,599 rounds off to 47,600.
So, 1,08,700 – 47,600 = 61,100
Rounding off to nearest tens:
1,08,734 rounds off to 1,08,730,
47,599 rounds off to 47,600.
So, 1,08,730 – 47,600 = 61,130
(c) 8325 – 491
Rounding off to nearest hundreds:
8325 rounds off to 8300,
491 rounds off to 500.
So, 8300 – 500 = 7800
Rounding off to nearest tens:
8325 rounds off to 8330,
491 rounds off to 490.
So, 8330 – 490 = 7840
(d) 4,89,348 – 48,365
Rounding off to nearest hundreds:
4,89,348 rounds off to 4,89,300,
48,365 rounds off to 48,400.
So, 4,89,300 – 48,400 = 4,40,900
Rounding off to nearest tens:
4,89,348 rounds off to 4,89,350,
48,365 rounds off to 48,370.
So, 4,89,350 – 48,370 = 4,40,980
3. Estimate the following products using the general rule:
(a) 578 × 161
(b) 5281 × 3491
(c) 1291 × 592
(d) 9250 × 29
(a) 578 × 161
(b) 5281 × 3491
(c) 1291 × 592
(d) 9250 × 29
Solutions:
(a) 578 × 161
Rounding off by the general rule:
578 rounds off to 600,
161 rounds off to 200.
So, 600 × 200 = 120,000
(b) 5281 × 3491
Rounding off by the general rule:
5281 rounds off to 5000,
3491 rounds off to 3500.
So, 5000 × 3500 = 17,500,000
(c) 1291 × 592
Rounding off by the general rule:
1291 rounds off to 1300,
592 rounds off to 600.
So, 1300 × 600 = 780,000
(d) 9250 × 29
Rounding off by the general rule:
9250 rounds off to 9000,
29 rounds off to 30.
So, 9000 × 30 = 270,000
(a) 578 × 161
Rounding off by the general rule:
578 rounds off to 600,
161 rounds off to 200.
So, 600 × 200 = 120,000
(b) 5281 × 3491
Rounding off by the general rule:
5281 rounds off to 5000,
3491 rounds off to 3500.
So, 5000 × 3500 = 17,500,000
(c) 1291 × 592
Rounding off by the general rule:
1291 rounds off to 1300,
592 rounds off to 600.
So, 1300 × 600 = 780,000
(d) 9250 × 29
Rounding off by the general rule:
9250 rounds off to 9000,
29 rounds off to 30.
So, 9000 × 30 = 270,000
