NCERT Class 6 Maths | Chapter 1 | Knowing Our Numbers
Practice problems and solutions for class 6 NCERT mathematics chapter 1 Knowing Our Numbers are given here.
CLASS 6 | CHAPTER 1 | KNOWING OUR NUMBERS
EXERCISE 1.1
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
Answers
a. Ten
b. Ten
c. Ten
d. Ten
e. Ten
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.
Answers
a. 73, 75,307
b. 9, 05, 00,041
c. 7, 52, 21,302
d. 58,423,202
e. 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
Answers
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 and one
4. Insert commas suitably and write the names according to International System of Numeration:
a. 78921092
b. 7452283
c. 99985102
d. 48049831
Answers
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 and two.
d. 48,049,831
Forty eight million forty nine thousand eight hundred and thirty one.
EXERCISE 1.2
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.
Ans.
The number of tickets sold on the first day = 1094
The number of tickets sold on the second day = 1812
The number of tickets sold on the third day = 2050
The number of tickets sold on the final day = 2751
So total number of tickets sold on all the 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?
Ans.
The runs scored by Shekhar in test matches = 6980
The runs he needed to complete 10,000 runs = 10,000 – 6980 = 3020 runs
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.
The votes secured by the successful candidate = 5, 77,500
The votes secured by the nearest rival = 3, 48, 700
Difference of votes = 5, 77,500 – 3, 48,700 = 2, 28,800 votes
4. Kirti bookstore sold books worth rupees 2, 85,891 in the first week of June and books worth rupees, 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?
Ans.
The amount spend in the first week of June = 2, 85,891
The amount spend in the second week of June = 4, 00,768
The total sale for the two weeks together = 2, 85,891 + 4, 00,768 = 6, 86, 659 rupees
In the second week the sale was greater.
Difference = 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.
Ans.
The greatest 5 digit number = 76,432
The least 5 digit number = 23,467
Difference = 76432 – 23467 = 52,965
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.
The number of screws manufactured a day = 2,825
The number of days in the month of January = 31
The number of screws produced in the month of January = 2,825 x 31 = 87,575 screws
7. A merchant had 78,592 rupees with her. She placed an order for purchasing 40 radio sets at 1200 rupees each. How much money will remain with her after the purchase?
Ans.
The cost of one radio set = 1200 rupees
The cost of 40 radio sets = 1200 x 40 = 48,000 rupees
Total money she has = 78,592
The amount of money remaining with her after the purchase = 78,592 – 48,000 = 30,592 rupees
8. A student multiplied 7236 by 65 instead of multiplying by 56.By how much was his answer greater than the correct answer?
Ans.
7236 x 65 = 470340
7236 x 56 = 405216
Difference = 470340 – 405216 = 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?
Ans
First convert data in cm
2 m 15 cm = 215 cm
40 m = 4000 cm
The number of shirts can be stitched = 4000 ÷ 215 = 18 shirts and 1 m 30 cm cloth will remain
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?
Ans.
First convert data in gram
4 kg 500 g = 4500 g
800 kg = 800000 g
Number of boxes that can be loaded in the van = 800000 ÷ 4500 = 177
Hence 177 boxes can be loaded in a van.
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?
Ans.
Distance between house and school = 1 km 875 m
1 km = 1000m
1 km 875 m = 1875 m
Distance covered every day = 1875 +1875 = 3750 m
Distance covered in 6 days = 3750 x 6 = 22500 m
Distance covered by her in six days = 22 km 500m
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.
The amount of curd in the vessel = 4 litre 500 ml = 4500 ml
Capacity of the glass = 25 ml
Number of glasses that can be filled = 4500 ÷25 = 180 glasses.
Exercise 1.3
1. Estimate each of the following using general rules:
a. 730 +998
b. 796 – 314
c. 12,904 + 2,888
d. 28,292 – 21,496
Ans.
a. 730 rounds off to 700
998 rounds off to 1000
Estimated sum = 700 + 1000 = 1700
b. 796 rounds off to 800
314 rounds off to 300
Estimated difference = 800 – 300 = 500
c. 12,904 rounds off to 13,000
2,888 rounds off to 3000
Estimated sum = 13,000+ 3000 = 16,000
d. 28,292 rounds off to 28000
21,496 rounds off to 21,000
Estimated difference = 28,000 – 21,000 = 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
Ans.
a. By rounding off to nearest hundreds:
439 rounds off to 400
334 rounds off to 300
4,317 rounds off to 4,300
Estimated sum = 400 + 300 + 4,300 = 5000
By rounding off to nearest tens:
439 rounds off to 440
334 rounds off to 330
4,317 rounds off to 4,320
Estimated sum = 440 + 330 + 4,320 = 5090
b. By rounding off to nearest hundreds:
1, 08,734 rounds off to 1, 08,700
47,599 rounds off to 47,600
Estimated difference = 1, 08,700 – 47,600 = 61100
By rounding off to nearest tens:
1, 08,734 rounds off to 1, 08,730
47,599 rounds off to 47,600
Estimated difference = 1, 08,730 – 47,600 = 61130
c. By rounding off to nearest hundreds:
8325 rounds off to 8300
491 rounds off to 500
Estimated difference = 8300 – 500 = 7800
By rounding off to nearest tens:
8325 rounds off to 8330
491 rounds off to 490
Estimated difference = 8330 –490= 7840
d. By rounding off to nearest hundreds:
4, 89,348 rounds off to 4, 89,300
48,365 rounds off to 48,400
Estimated difference = 4, 89,300 – 48,400 = 440900
By rounding off to tens:
4, 89,348 rounds off to 4, 89,350
48,365 rounds off to 48,370
Estimated difference = 4, 89,350 – 48,370 = 440980
3. Estimate the following products using general rule:
a. 578 x 161
b. 5281 x 3491
c. 1291 x 592
d. 9250 x 29
Ans.
a. 578 rounds off to 600
161 rounds off to 200
The estimated product = 600 x 200 = 120000
b. 5281 rounds off to 5000
3491 rounds off to 3500
Estimated product = 3500 x 5000 = 1, 75, 00,000
c. 1291 rounds off to 1300
592 rounds off to 600
Estimated product = 1300 x 600 =7, 80,000
d. 9250 rounds off to 10,000
29 rounds off to 30
Estimated product = 10,000 x 30 = 3, 00,000
Roman Numerals:
One of the early systems of writing numerals is the system of Roman numerals.
The Roman numerals I,II,III,IV,V,VI,VII,VIII,IX,X denote 1,2,3,4,5,6,7,8,9,10 respectively. This is followed by XI for 11, XII for 12,……… till XX for 20.
Some more Roman numerals are:
L = 50
C =100
D = 500
M = 1000
Also X =10
XX =20
XXX =30
XL =40
L = 50
LX = 60
LXX = 70
LXXX = 80
XC = 90
C =100
1. Write in Roman numerals:
a. 69
b.98
Ans.69 = 60+9 = (50 + 10) +9 = LX +IX = LXIX
98 = 90 + 8 = (100 – 10)+8 = XC + VIII = XCVIII
