Chapter 1: Knowing Our Numbers
Ex- 1.1
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 = _______ lakh.
Solution:
- 1 lakh = 10 ten thousand. (10*10000 = 1000000)
- 1 million = 10 hundred thousand. (10*100000 = 1000000)
- 1 crore = 10 ten lakhs. (10*1000000 = 10000000)
- 1 crore = 10 million. (10*1000000 =10000000)
- 1 million = 10 lakh. (10*100000 = 1000000)
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:
- 73,75,307.
- 9,05,00,041.
- 7,52,21,302.
- 58,423,202.
- 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
Solution:
- Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two.
- Eighty-five lakh forty-six thousand two hundred eighty-three.
- Nine crore ninety-nine lakhs forty-six.
- Nine crore eighty-four lakh thirty-two thousand seven hundred one.
4. Insert commas suitably and write the names according to International System of Numeration:
(a) 78921092 (b) 7452283 (c) 99985102 (d) 48049831
Solution:
- 78,921,092
Seventy-eight million night hundred twenty-one thousand ninety-two.
2. 7,452,283
Seven million four hundred fifty-two thousand two hundred eighty-three.
3. 99,985,102
Ninety-nine million nine hundred eighty-five thousand one hundred two.
4. 48,049,831
Forty-eight million forty-nine thousand eight hundred thirty-one.
EXERCISE 1.2
- 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:
First day = 1094
Second day =1812
Third day = 2050
Final day = 2751
Total ticket = 1094+1812+2050+2751
= 7707
2. Shear 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:
Runs scored by Shear = 6980
Runs he wishes to score = 10,000
Number of runs need = 10,000 – 6980
= 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?
Solution:
Votes of successful candidate = 5,77,500
Votes of nearest rival = 3,48,700
Margin of winning election = 5,77,500 – 3,48,700
= 2,28,800
4. Kirri 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?
Solution:
First week = 2,85,891
Second week = 4,00,768
The sale of two weeks together = 2,85,891 + 4,00,768
= 6,86,659
Since,
4,00768 > 2,85,891
Second week is greater than first week because
= 4,00,768 – 2,85,891
= 1,14,877
5. Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once
Solution:
Greatest = 76432
Smallest = 23467
Difference = 76432 – 23467
= 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?
Solution:
Screws produced in 1 day = 2,825
Screws produced in 31 days = 2,825 * 31
= 87,575
[ We known that in January 2006 total day = 31]
Total screws produced in 31 days is 87,575. ANS
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?
Solution:
Total money merchant has = RS. 78,592
She needs to purchase radio = 40
Cost price of 1 radio = RS. 1200
Therefore, cost price of 40 radio = RS. 1200 * 40
= RS. 48000
Now, she has left money =RS. 78,592 – RS. 48,000
= 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? (Hint: Do you need to do both the multiplications?)
Solution:
Multiplication = 7236
Done before = 7236* 65
= 3,70,340 (incorrect)
Again,
Multiplication = 7236
Done before = 7236 *56
=4,05,216 (correct)
= 4,70,340 – 4,05,216
= 65,124.
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? (Hint: convert data in cm.)
Solution:
Total length of cloth = 40m
Let no. of shirts = x
1 shirt = 2m15cm
Therefore, x shirts = 2m15cm*x
2m15cm*x = 40m
x = 40m/2m15cm
Now, we convert m into cm
x = 4000/215 cm
x = 18
18 shirts can be made & 130 cm cloth are left
130cm = 1m30cm.
10. Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?
Solution:
Total weight van can carry =800kg
Weight of one box = 4kg500g
Let no. of box to carry in van = x
Weight of 1 box = 4kg500g
So, weight of x boxes = x*4kg500g
x*4kg500g = 800kg
x = 800kg/4kg500g
Now, we convert kg in g
x 800,000/4500 g
x = 177
11. The distance between the school and 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:
Distance of her in going from home to school = 1km875m
Distance of her in going from school to home = 1km875m
Total distance = 1km875m+1km875m
= 3km750m
Distance of her in 6 days = total distance * 6
= 3km750*6
= 22km500m.
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:
Total curd = 4l 500ml
Curd n 1 glass =25ml
Let total glass can fill a vessel = x
Therefore,
Curd in x glass = 25*xml
25xml = 4l 500ml
x = 4l 500ml /25ml
Now, we convert l in ml
x = 4500ml/25ml
x = 180 Ml.
EXERCISE 1.3
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
Make ten more such examples of addition, subtraction and estimation of their outcome.
Solution:
a. 730 + 998
= 700 + 1000 [ we use nearest hundred]
= 1700
b. 796 – 314
= 800 – 300 [we use nearest hundred]
= 500
c. 12,904 + 2,888
= 13000 + 3000 [ we use nearest thousand]
= 16000
d. 28292 – 21496
= 28000 – 21000 [ we use nearest thousand]
= 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
Make four more such examples.
Solution:
a. 439 + 334 + 4,317
By nearest hundred
= 439 + 334 + 4,317
= 400 + 300+ 4,300
= 5,000
By nearest tens
= 439 + 334 + 4,317
= 440 + 330 + 4,320
= 5,090
b. 1,08,734 – 47,599
By nearest hundred
= 1,08,734 – 47,599
= 1,08,700 – 47,600
= 61,100
By nearest tens
= 1,08,734 – 47,599
= 1,08,730 – 47,600
= 61,130
c. 8,325 – 491
By nearest hundred
= 8,325 – 491
= 8,300 – 500
= 7,840
By nearest tens
= 8,325 – 491
= 8,330 – 490
= 7,840
d. 4,89,348 – 48,365
By nearest hundred
= 4,89,348 – 48,365
= 4,89,300 – 48,400
= 4,40,900
By nearest tens
= 4,89,348 – 48,365
= 4,89,350 – 48,370
= 4,40,980
3. Estimate the following products using general rule:
(a) 578 × 161 (b) 5281 × 3491 (c) 1291 × 592 (d) 9250 × 29
Make four more such examples.
Solution:
a. 578 * 161
= 600 * 200
=1,20,000
b. 5,281 * 3,491
= 5,000 * 3,500
= 1,75,00,000
c. 1,291 * 592
= 1300 * 600
= 7,80,000
d.9,250 * 29
= 9,000 * 30
=2,70,000
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