Question Answer For All Chapters – Ganita Prakash Class 7th
Large Numbers Around Us
Page 2
1. What if a person ate 3 varieties of rice every day? Will they be able to taste all the lakh varieties in a 100 year lifetime? Find out.
Ans: Varieties of rice eaten per day = 3
Number of days in 1 year = 365
So, rice varieties eaten in 1 year =
3 × 365 = 1,095 varieties
Now, rice varieties eaten in 100 years =
1,095 × 100 = 1,09,500 varieties
Yes, the person can taste all 1 lakh varieties of rice in 100 years.
2. Choose a number for y. How close to one lakh is the number of days in y years, for the y of your choice?
Ans: Let’s choose y = 274 years
Now calculate:
365 × 274 = 1,00,010 days
This is 10 days more than 1 lakh.
Let’s check for y = 273 years
365 × 273 = 99,645 days
This is 355 days less than 1 lakh.
At y = 274, we get 1,00,010 days, which is closest to 1 lakh.
So, y = 274 years gives a lifetime that is very close to 1 lakh days.
Figure it Out (Page 3)
1. According to the 2011 Census, the population of the town of Chintamani was about 75,000. How much less than one lakh is 75,000?
Ans: One lakh = 1,00,000
Population = 75,000
Now subtract:
1,00,000 − 75,000 = 25,000
75,000 is 25,000 less than one lakh.
2. The estimated population of Chintamani in 2024 is 106,000. How much more than one lakh is 1,06,000?
Ans: One lakh = 1,00,000
Estimated population = 1,06,000
Now subtract:
1,06,000 − 1,00,000 = 6,000
1,06,000 is 6,000 more than one lakh.
3. By how much did the population of Chintamani increase from 2011 to 2024?
Ans: Population in 2011 = 75,000
Estimated population in 2024 = 1,06,000
1,06,000 − 75,000 = 31,000
The population of Chintamani increased by 31,000 from 2011 to 2024
Getting a Feel of Large Numbers – Page 3
Look at the picture on the right. Somu is 1 metre tall. If each floor is about four times his height, what is the approximate height of the building?
Ans: Somu’s height = 1 meter.
Each floor ≈ 4 × 1 = 4 meters.
The building in the picture has 10 floors.
Height of building = 11 × 4 = 40 meters.
Approximately 44 meters.
1. Which is taller — The Statue of Unity or this building? How much taller? __________ m
Ans: The height of the Statue of Unity is 180 metres, and the height of the building is 44 metres.
To find how much taller the statue is, we subtract:
180 − 44 = 136 metres
So, the Statue of Unity is 136 metres taller than the building.
2. How much taller is the Kunchikal waterfall than Somu’s building? __________ m
Ans: Height of Kunchikal waterfall = 450 metres
Height of Somu’s building = 44 metres
450 − 44 = 406 metres
3. How many floors should Somu’s building have to be as high as the waterfall?
Ans: Height of Kunchikal waterfall = 450 metres
Each floor of Somu’s building = 4 metres
Calculation: 450 ÷ 4 = 112.5
Somu’s building should have 113 floors to be as high as the Kunchikal waterfall.
Is One Lakh a Very Large Number? Page – 4
How do you view a lakh — is a lakh big or small?
Ans: A lakh can feel big or small depending on the situation:
It feels big when we talk about money, varieties of rice, or living 1 lakh days.
It feels small when we talk about stadium capacity, number of hairs, or fish eggs.
Reading and Writing Numbers (Pages 4-5)
1. Write each of the numbers given below in words:
(a) 3,00,600
(b) 5,04,085
(c) 27,30,000
(d) 70,53,138
Ans: (a) 3,00,600 → Three lakh six hundred
(b) 5,04,085 → Five lakh four thousand eighty-five
(c) 27,30,000 → Twenty-seven lakh thirty thousand
(d) 70,53,138 → Seventy lakh fifty-three thousand one hundred thirty-eight
2. Write the corresponding number in the Indian place value system for each of the following:(a) One lakh twenty three thousand four hundred and fifty six
(b) Four lakh seven thousand seven hundred and four
(c) Fifty lakhs five thousand and fifty
(d) Ten lakhs two hundred and thirty five
Ans: (a) 1,23,456
(b) 4,07,704
(c) 50,05,050
(d) 10,00,235
1.2 Land of Tens (Page 5-6)
1. The Thoughtful Thousands only has a +1000 button. How many times should it be pressed to show:
(a) Three thousand? 3 times
(b) 10,000? ____________
(c) Fifty three thousand? ___________
(d) 90,000? ______________
(e) One Lakh? ________________
(f) ____________? 153 times
(g) How many thousands are required to make one lakh?
Ans: (a) Three thousand → 3 times (Already given)
(b) 10,000 ÷ 1000 = 10 times
(c) 53,000 ÷ 1000 = 53 times
(d) 90,000 ÷ 1000 = 90 times
(e) 1,00,000 ÷ 1000 = 100 times
(f) 153 × 1000 = 1,53,000
(g) To make one lakh:
1,00,000 ÷ 1000 = 100 thousands
2. The Tedious Tens only has a +10 button. How many times should it be pressed to show:
(a) Five hundred? _____________
(b) 780? _________
(c) 1000? _________
(d) 3700? ________
(e) 10,000? ___________
(f) One lakh? _____________
(g) ____________? 435 times
Ans: (a) 500 ÷ 10 = 50 times
(b) 780 ÷ 10 = 78 times
(c) 1000 ÷ 10 = 100 times
(d) 3700 ÷ 10 = 370 times
(e) 10,000 ÷ 10 = 1000 times
(f) 1,00,000 ÷ 10 = 10,000 times
(g) 435 × 10 = 4350
3. The Handy Hundreds only has a +100 button. How many times should it be pressed to show:
(a) Four hundred? __________ times
(b) 3,700? __________
(c) 10,000? __________
(d) Fifty-three thousand? __________
(e) 90,000? __________
(f) 97,600? __________
(g) 1,00,000? __________
(h) __________? 582 times
(i) How many hundreds are required to make ten thousand?
(j) How many hundreds are required to make one lakh?
(k) Handy Hundreds says, “There are some numbers which Tedious Tens and Thoughtful Thousands can’t show but I can.” Is this statement true? Think and explore.
Ans: (a) 400 ÷ 100 = 4 times
(b) 3,700 ÷ 100 = 37 times
(c) 10,000 ÷ 100 = 100 times
(d) 53,000 ÷ 100 = 530 times
(e) 90,000 ÷ 100 = 900 times
(f) 97,600 ÷ 100 = 976 times
(g) 1,00,000 ÷ 100 = 1000 times
(h) 582 × 100 = 58,200
(i) To make 10,000 → 100 hundreds
(j) To make 1,00,000 → 1000 hundreds
(k) Yes, it’s true.
For example, to show 510, you can press:
5 × 100 + 1 × 10, which Tedious Tens can do.
But Thoughtful Thousands cannot show it.
For 550, Tedious Tens would need 55 presses, but Handy Hundreds can do it in 5.5 presses — which it can’t actually perform without decimals.
However, Handy Hundreds can represent values that neither of the other two can do efficiently or exactly.
4. Creative Chitti is a different kind of calculator. It has the following buttons: +1, +10, +100, +1000, +10000, +100000 and +1000000. It always has multiple ways of doing things. “How so?”, you might ask. To get the number 321, it presses +10 thirty two times and +1 once. Will it get 321? Alternatively, it can press +100 two times and +10 twelve times and +1 once.
Ans:
Way 1:
- Press +10 button 32 times = 32 × 10 = 320
- Press +1 button 1 time = 1
- 320 + 1 = 321
- Yes, this gives 321
Way 2:
- Press +100 button 2 times = 2 × 100 = 200
- Press +10 button 12 times = 12 × 10 = 120
- Press +1 button 1 time = 1
- 200 + 120 + 1 = 321
- This also gives 321
5. Two of the many different ways to get 5072 are shown below:
These two ways can be expressed as:
(a) (50 × 100) + (7 × 10) + (2 × 1) = 5072
(b) (3 × 1000) + (20 × 100) + (72 × 1) = 5072
Find a different way to get 5072 and write an expression for the same.
Ans: Here, (5 × 1000) + (0 × 100) + (7 × 10) + (2 × 1)
= 5000 + 0 + 70 + 2
= 5072
Figure it Out (Page 6-7)
For each number given below, write expressions for at least two different ways to obtain the number through button clicks. Think like Chitti and be creative.
(а) 8300
(b) 40629
(c) 56354
(d) 66666
(e) 367813
Ans: (a) 8300
Way 1:
= 8 × 1000 + 3 × 100
= 8000 + 300 = 8300
Way 2:
= 83 × 100
= 8300
(b) 40629
Way 1:
= 4 × 10000 + 0 × 1000 + 6 × 100 + 2 × 10 + 9 × 1
= 40000 + 0 + 600 + 20 + 9 = 40629
Way 2:
= 40 × 1000 + 600 + 20 + 9
= 40000 + 600 + 20 + 9 = 40629
(c) 56354
Way 1:
= 5 × 10000 + 6 × 1000 + 3 × 100 + 5 × 10 + 4 × 1
= 50000 + 6000 + 300 + 50 + 4 = 56354
Way 2:
= 56 × 1000 + 3 × 100 + 5 × 10 + 4
= 56000 + 300 + 50 + 4 = 56354
(d) 66666
Way 1:
= 6 × 10000 + 6 × 1000 + 6 × 100 + 6 × 10 + 6
= 60000 + 6000 + 600 + 60 + 6 = 66666
Way 2:
= 66 × 1000 + 666
= 66000 + 666 = 66666
(e) 367813
Way 1:
= 3 × 100000 + 6 × 10000 + 7 × 1000 + 8 × 100 + 1 × 10 + 3
= 300000 + 60000 + 7000 + 800 + 10 + 3 = 367813
Way 2:
= 36 × 10000 + 7813
= 360000 + 7813 = 367813
Page – 7
1. Creative Chitti has some questions for you-
(a) You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make?
Ans: (a) For the largest 3-digit number:
Press the +100 button 9 times: 9 × 100 = 900
Add 10 more presses using the +10 button: 10 × 10 = 100
Add the remaining 11 presses using the +1 button: 11 × 1 = 11
Sum: 900 + 100 + 11 = 1011, but that’s a 4-digit number.
Scale back by reducing the number of +10 presses to 8 and +1 presses to 13.
Largest 3-digit number: 993 (9 × 100 + 8 × 10 + 13 × 1)
For the smallest 3-digit number
Press the +10 button 8 times: 8 × 10 = 80
Add 22 more presses using the +1 button: 22 × 1 = 22
Smallest 3-digit number: 102 (8 × 10 + 22 × 1)
(b) 997 can be made using 25 clicks. Can you make 997 with a different number of clicks?
Ans: 9 × (+100) = 900
8 × (+10) = 80
17 × (+1) = 17
Figure it Out (Page – 7)
1. For the numbers in the previous exercise, find out how to get each number by making the smallest number of button clicks and write the expression.
Ans: (a) Here, 8300
(8 × 1,000) + (3 × 100) = 8300
Hence, 8300 can be obtained in 8 + 3 = 11 clicks.
(b) Here, 40629
(4 × 10,000) + (6 × 100) + (2 × 10) + (9 × 1) = 40629
Hence, 40629 can be obtained in 4 + 6 + 2 + 9 = 21 clicks.
(c) Here, 56354
(5 × 10,000) + (6 × 1,000) + (3 × 100) + (5 × 10) + (4 × 1) = 56354
Hence, 56354 can be obtained in 5 + 6 + 3 + 5 + 4 = 23 clicks.
(d) Here, 66666
(6 × 10,000) + (6 × 1,000) + (6 × 100) + (6 × 10) + (6 × 1) = 66666
Hence, 66666 can be obtained in 6 + 6 + 6 + 6 + 6 = 30 clicks.
(e) We have 367813
(3 × 1,00,000) +(6 × 10,000) + (7 × 1,000) + (8 × 100) + (1 × 10) + (3 × 1) = 367813
Hence, 367813 can be obtained in 3 + 6 + 7 + 8 + 1 + 3 = 28 clicks.
2. Do you see any connection between each number and the corresponding smallest number of button clicks?
Ans: Yes, there is a clear connection:
The smallest number of button clicks needed to make a number depends directly on its place values — that is, how many non-zero digits the number has and in which places.
3. If you notice, the expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so.
Ans: Yes, this is true — and here’s why:
When we express a number using the fewest button clicks, we break it into its place values:
- Lakh
- Ten-thousand
- Thousand
- Hundred
- Ten
- One
These are exactly the same place values used in the Indian place value system.
Of Crores and Crores! (Page – 8, 9)
1. How many zeros does a thousand lakh have? _____
Ans: 1,000 lakh = 10,00,00,000 (8 zeros)
2. How many zeros does a hundred thousand have?
Ans: 100 thousand = 1,00,000 (5 zeros)
Figure it Out (Page 9)
1. Read the following numbers in Indian place value notation and write their number names in both the Indian and American systems:
(a) 4050678 (b) 48121620
(c) 20022002 (d) 246813579
(e) 345000543 (f) 1020304050
Ans: (a) 4050678
- Indian notation: 40,50,678
- Indian system name: Forty lakh fifty thousand six hundred seventy-eight
- American notation: 4,050,678
- American system name: Four million fifty thousand six hundred seventy-eight
(b) 48121620
- Indian notation: 4,81,21,620
- Indian system name: Four crore eighty-one lakh twenty-one thousand six hundred twenty
- American notation: 48,121,620
- American system name: Forty-eight million one hundred twenty-one thousand six hundred twenty
(c) 20022002
- Indian notation: 2,00,22,002
- Indian system name: Two crore twenty-two thousand two
- American notation: 20,022,002
- American system name: Twenty million twenty-two thousand two
(d) 246813579
- Indian notation: 24,68,13,579
- Indian system name: Twenty-four crore sixty-eight lakh thirteen thousand five hundred seventy-nine
- American notation: 246,813,579
- American system name: Two hundred forty-six million eight hundred thirteen thousand five hundred seventy-nine
(e) 345000543
- Indian notation: 34,50,00,543
- Indian system name: Thirty-four crore fifty lakh five hundred forty-three
- American notation: 345,000,543
- American system name: Three hundred forty-five million five hundred forty-three
(f) 1020304050
- Indian notation: 1,02,03,04,050
- Indian system name: One arab two crore three lakh four thousand fifty
- American notation: 1,020,304,050
- American system name: One billion twenty million three hundred four thousand fifty
2. Write the following numbers in Indian place value notation:
(a) One crore one lakh one thousand ten
(b) One billion one million one thousand one
(c) Ten crore twenty lakh thirty thousand forty
(d) Nine billion eighty million seven hundred thousand six hundred
Ans: (a) 1,01,01,010
(b) 1,001,001,001
(c) 10,20,30,040
(d) 9,080,700,600
3. Compare and write ‘<’, ‘>’ or ‘=’:
(a) 30 thousand ____ 3 lakhs
(b) 500 lakhs ______ 5 million
(c) 800 thousand ____ 8 million
(d) 640 crore ______ 60 billion
(a) 30 thousand ____ 3 lakhs
Ans: 30 thousand = 30,000
- 3 lakhs = 3,00,000
- 30,000 < 3,00,000
(b) 500 lakhs ______ 5 million
Ans:
- 1 million = 10 lakhs
- So, 5 million = 50 lakhs
- 500 lakhs > 50 lakhs
(c) 800 thousand ____ 8 million
Ans:
- 800 thousand = 800,000
- 8 million = 8,000,000
- 800,000 < 8,000,000
(d) 640 crore ______ 60 billion
Ans:
- 1 billion = 100 crore
- So, 60 billion = 60 × 100 = 6,000 crore
- 640 crore < 6,000 crore
Nearest Neighbours (Pages 11-12)
1. write the five nearest neighbours for these numbers:
(a) 3,87,69,957
(b) 29,05,32,481
Ans: (a) 3,87,69,957
- Nearest thousand → 3,87,70,000
- Nearest ten thousand → 3,87,70,000
- Nearest lakh → 3,88,00,000
- Nearest ten lakh → 3,90,00,000
- Nearest crore → 4,00,00,000
(b) 29,05,32,481
- Nearest thousand → 29,05,32,000
- Nearest ten thousand → 29,05,30,000
- Nearest lakh → 29,05,00,000
- Nearest ten lakh → 29,10,00,000
- Nearest crore → 29,00,00,000
Figure it Out (Page 11)
1. 4,63,128 + 4,19,682,
Roxie: “The sum is nearly 8,00,000 and is more than 8,00,000.”
Estu: “The sum is nearly 9,00,000 and is less than 9,00,000.”
(a) Are these estimates correct? Whose estimate is closer to the sum?
(b) Will the sum be greater than 8,50,000 or less than 8,50,000? Why do you think so?
(c) Will the sum be greater than 8,83,128 or less than 8,83,128? Why do you think so?
(d) Exact value of 4,63,128 + 4,19,682 = _____________
Ans: (a) By adding 4,63,128 and 4,19,682, we get 8,82,810 and the estimated sum is 5,00,000 + 4,00,000 = 9,00,000
The exact sum is 8,82,810, which is closer to 9,00,000.
Thus, Estu’s estimate is correct and closer to the actual sum.
(b) The exact sum is 8,82,810, which is clearly greater than 8,50,000.
If we estimate the two numbers (4,63,128 and 4,19,682) to the nearest ten thousands, we get 4,60,000 and 4,20,000.
By adding them, the results will be closer to 8,80,000, which is well above 8,50,000.
(c) The exact sum is 8,82,810, which is less than 8,83,128.
The sum falls short of 8,83,128 by only 318, making it closer to the actual sum.
(d) Exact value of 4,63,128 + 4,19,682 = 8,82,810
2. 14,63,128 – 4,90,020
Roxie: “The difference is nearly 10,00,000 and is less than 10,00,000.”
Estu: “The difference is nearly 9,00,000 and is more than 9,00,000”.
(a) Are these estimates correct? Whose estimate is closer to the difference?
(b) Will the difference be greater than 9,50,000 or less than 9,50,000? Why do you think so?
(c) Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think so?
(d) Exact value of 14,63,128 – 4,90,020 = ___________
Ans: (a) Exact difference = 14,63,128 – 4,90,020 = 9,73,108
Estimated difference = 15,00,000 – 5,00,000 = 10,00,000
Roxie’s estimate is closer to the actual difference.
(b) Exact difference = 9,73,108
It is greater than 9,50,000.
Now estimating the numbers 14,63,128 and 4,90,020 to the nearest ten thousands place, we get 14,60,000 and 4,90,000 respectively.
Now, Difference = 14,60,000 – 4,90,000 = 9,70,000
It is more than 9,50,000.
(c) Exact difference is 9,73,108
It is greater than 9,63,128.
Difference = 9,73,108, – 9,63,128 = 9,980
It is far from the actual difference.
(d) Exact value = 14,63,128 – 4,90,020 = 9,73,108
Population of Cities (Pages 12-13)
1. What is your general observation about this data? Share with the class.
Ans: The population of all 20 cities has increased between 2001 and 2011.
2. What is an appropriate title for the above table?
Ans: “Population Growth of Indian Cities (2001–2011)”
3. How much is the population of Pune in 2011? Approximately, by how much has it increased compared to 2001?
Ans: Population of Pune in 2011 = 31,15,431 and in 2001 = 25,38,473
Approximate Increase in population: 31,00,000 – 25,00,000 = 6,00,000
4. Which city’s population increased the most between 2001 and 2011?
Ans: Bengaluru experienced the largest population increase, with a growth of 41,24,644 people.
5. Are there cities whose population has almost doubled? Which are they?
Ans: Bengaluru, Hyderabad, Surat, Vadodara, and Pimpri-Chinchwad nearly doubled their population between 2001 and 2011.
6. By what number should we multiply Patna’s population to get a number/population close to that of Mumbai?
Ans: Mumbai’s population by Patna’s population in 2011 =\( \frac{1,24,42,373}{16,84,222}\) ~ 7
Patna’s population needs to be multiplied by 7 to be close to Mumbai’s population.
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