1 KNOWING OUR NUMBERS

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1 1 KNOWING OUR NUMBERS Q.1. Fill in the blanks : (a) 1 lakh Exercise 1.1 = ten thousand. (b) 1 million = hundred thousand. (c) 1 crore (d) 1 crore = ten lakh. = million. (e) 1 million = lakh. Ans. (a) 10 (b) 10 (c) 10 (d) 10 (e) 10. Q.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 Q.3. Insert commas suitably and write the names according to Indian System of Numeration : (a) (b) (c) (d)

2 Ans. Number Number Name (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. Q.4. Insert commas suitably and write the names according to International System of Numeration : (a) (b) (c) (d) Ans. Number Number Name (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 millions, forty-nine thousand, eight hundred thirty one. Exercise 1.2 Q.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 Find the total number of tickets sold on all the four days. Ans. Tickets sold on the first day = 1094 Tickets sold on the second day =

3 Tickets sold on the third day = 2050 Tickets sold on the fourth day = 2751 Total number of tickets sold on all the four days = = 7707 Q.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. Shekhar wishes to complete = 10,000 runs Shekhar has so far scored = 6,980 runs Number of more runs he needs = (10,000 6,980) runs = 3,020 runs. Q.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. Number of votes registered by successful candidate = 5,77,500 Number of votes secured by his nearest rival candidate = 3,48,700 Successful candidate win the election by (5,77,500 3,48,700) votes = 2,28,800 votes. Q.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? 3

4 Ans. Case I Books sold in the first week of June = Rs 2,85,891 Books sold in the second week of June = Rs 4,00,768 So, total sale for the two weeks of June = Rs (2,85, ,00,768) = Rs 6,86,659 Case II On comparing the sales, sale was greater in second week of June. Sale in the second week is greater by Rs (4,00,678 2,85,891) = Rs 1,14,877 Q.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. Ans. Given digits are 6, 2, 7, 4, 3 These numbers in descending order are 7, 6, 4, 3 and 2 Hence the greatest number = 76,432 These numbers in ascending order are 2, 3, 4, 6 and 7 Hence, the least number = 23,467 Difference between the greatest and the least number = 76,432 23,467 = 52,965 Ans. Q.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. We know, number of days in the month of January 2006 = 31 days Therefore, number of screws produced in 31 days 4

5 = 31 2,825 = 87,575 screws. Q.7. A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1,200 each. How much money will remain with her after the purchase? Ans. Total money, the merchant had = Rs 78,592 Value of 1 Radio set = 1 1,200 = Rs 1,200 (given) Similarly, Value of 40 Radio sets = 40 1,200 = Rs 48,000 Money remaining with the merchant Total money with the merchant Value of 40 Radio sets = Rs (78,592 48,000) = Rs 30,592 Hence, remaining money with the merchant is Rs. 30,592. Q.8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? Ans. Case I Case II 7,236 7, As per condition Case I is greater by :

6 Hence, the new answer is 65,124 more than the correct answer. Alternative method : The difference between 65 and 56 = = 9 Therefore, his answer is greater than the correct answer by = 65,124 Here, we do not need to do both the multiplications. Q.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 cloth = 40 m = cm = 4000 cm Cloth needed to stitch one shirt = 2 m 15 cm = ( ) cm = ( ) cm = 215 cm Number of shirts can be stitched Total length of cloth = Cloth needed to stitch one shirt 4000 cm = 215 cm 6

7 Hence, 18 shirts can be stitched and 1 m 30 cm cloth will remain. Q.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. Limit of van = 800 kg [1 kg = 1000 g] = g = 8,00,000 g Limit of 1 medicine box = 4 kg 500 g = 4, = 4,500 g Number of medicine boxes can be loaded in the van Limit of van = Limit of 1 medicine box 8,00,000 = 4,500 Hence, 177 medicine boxes can be loaded in the van. Q.11. The distance between the school and the student's house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days. Ans. Distance between the school and the house = 1 km 875 m (1 km = 1000 m) = [1000 m m] = 1875 m 7

8 One way distance = 1875 m Two way distance = m = 3750 m Distance covered by her in 1 day = Two way distance = 3750 m Distance covered by her in 6 days = m = 22,500 m = 22 km 500 m Hence total distance covered by her in 6 days is 22 km 500 m. Ans. Q.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. Total volume of curd = 4 l and 500 ml = = 4,500 ml Capacity of one glass = 25 ml Volume of curd Number of glasses = Capacity of one glass [1l = 1000 ml] 450 = = Hence, 180 glasses can be filled by curd. 8

9 Exercise 1.3 Q.1. Estimate each of the following using general rule : (a) (b) (c) 12, ,888 (d) 28,292 21,496 Ans. (a) Round off to hundreds 730 is rounded to is rounded to + 1,000 So, estimated sum = 1,700 (b) Round off to hundreds 796 is rounded to is rounded to 300 So, estimated difference = 500 (c) 12, ,888 Round off to thousands 12,904 is rounded to 13,000 +2,888 is rounded to + 3,000 So, estimated sum = 16,000 (d) 28,292 21,496 Round off to thousands 28,292 is rounded to 28,000 21,496 is rounded to 21,000 Thus, estimated difference = 7,000 Q.2. Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens) : 9

10 (a) ,317 (b) 1,08,734 47,599 (c) 8, (d) 4,89,348 48,365 Ans. (a) Rough estimate ,317 Round off to hundred = ,300 = 5,000 Closer estimate ,317 Round off to tens = ,317 = ,320 = 5,090 (b) Rough estimate 1,08,734 47,599 Round off to hundreds = 1,08,700 47,600 = 61,100 Closer estimate 1,08,734 47,599 Round off to tens = 61,130 (c) Rough estimate 8, = 1,08,730 47,600 Round off to hundreds = 8, =

11 Closer estimate 8, Round off to tens = 8, = 7,840 (d) Rough estimate 4,89,348 48,365 Round off to hundreds = 4,89,300 48,400 = 4,40,900 Closer estimates 4,89,348 48,365 Round off to tens = 4,89,350 48,370 = 4,40,980 Q.3. Estimate the following products using general rule : (a) (b) (c) (d) Ans. (a) 578 rounded off to hundreds = rounded off to hundreds = 200 Estimate product = 1,20,000 (b) 5,281 rounded off to thousands = 5,000 3,491 rounded off to hundreds = 3,500 Estimate product = = 1,75,00,000 11

12 (c) 1291 rounded off to hundreds = rounded off to hundreds = 600 Estimate products = = 7,80,000 (d) 9,250 rounded off to thousands = is rounded off to tens = 30 Estimate product = = 2,70,000 12

NCERT solution for Knowing our Numbers

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