Use the textbook context
Match, attempt, then check
Each crop extends to the next solved item, so diagrams, tables and connected instructions stay with the question.
Complete worked answers
Textbook page 2
Textbook page 2 · solved item 1
What if we ate 2 varieties of rice every day? Would we then be able to eat 1 lakh varieties of rice in 100 years?
Show solution
Days in a year = 365 Rice varieties eaten per day = 2 Rice varieties eaten in a year = 2×365 = 730 Rice varieties eaten in 100 years = 730×100 = 73,000 varieties. No, we can eat only 73,000 varieties in 100 years, not 1 lakh.
Textbook page 2 · solved item 2
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.
Show solution
Days in a year = 365 Rice varieties eaten per day = 3 Rice varieties eaten in a year = 3 × 365 = 1095 Rice varieties eaten in 100 years = 1095 × 100 = 1,09,500 varieties. Yes, they can eat all 1 lakh varieties in 100 years.
Textbook page 2 · solved item 3
Estu said, “We know how many days there are in a year — 365, if we ignore leap years. If we live for y years, the number of days in our lifetime will be 365 × y.” Choose a number for y. How close to one lakh is the number of days in y years, for the y of your choice?
Show solution
Assume we live for 95 years, i.e. y = 95. Number of days in our lifetime = 365 × 95 = 34,675 Difference between 1,00,000 and 34,675 = 1,00,000 – 34,675 = 65,325. Figure it Out
Complete worked answers
Textbook page 3
Textbook page 3 · solved item 4
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?
Show solution
Population of the town in 2011 = 75,000 Since 1,00,000 – 75,000 = 25,000 75,000 is 25,000 less than one lakh.
Textbook page 3 · solved item 5
2. The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?
Show solution
Population of town in 2024 = 1,06,000 Since, 1,06,000 – 1,00,000 = 6,000 1,06,000 is 6,000 more than one lakh.
Textbook page 3 · solved item 6
3. By how much did the population of Chintamani increase from 2011 to 2024?
Show solution
Increase in population from 2011 to 2024 = 1,06,000 – 75,000 = 31,000.
Textbook page 3 · solved item 7
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?
Show solution
Somu’s height = 1 metre Height of each floor = 4×1 = 4 metres Number of floors in the building = 10 Height of the building = 10×4 = 40 metres.
Textbook page 3 · solved item 8
Which is taller — The Statue of Unity or this building? How much taller? ____________m.
Show solution
Height of The Statue of Unity = 180 m Height of Somu’s building = 40 m Since, 180 – 40 = 140 m The Statue of Unity is 140 m taller than the building.
Textbook page 3 · solved item 9
How much taller is the Kunchikal waterfall than Somu's building? ____________m.
Show solution
Height of the Kunchikal waterfall = 450 m Height of Somu’s building = 40 m Since 450 – 40 = 410 m The Kunchikal waterfall is 410 m taller than Somu’s building.
Textbook page 3 · solved item 10
How many floors should Somu’s building have to be as high as the waterfall?
Show solution
Height of each floor in the building = 4 m Height of the waterfall = 450 m Number of floors required = 450 ÷ 4 = 112.5 So, Somu’s building should have at least 113 floors to be as high as the waterfall.
Complete worked answers
Textbook page 4
Textbook page 4 · solved item 11
How do you view a lakh — is a lakh big or small?
Show solution
A lakh can seem big or small depending on the context and what it's being compared to. For instance, a crowd of 1 lakh people at an event or protest is massive, but in terms of city population, 1 lakh might be considered a small town.
Textbook page 4 · solved item 12
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
Show solution
(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 and thirty eight.
Complete worked answers
Textbook page 5
Textbook page 5 · solved item 13
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
Show solution
(a) One lakh twenty three thousand four hundred and fifty six – 1,23,456. (b) Four lakh seven thousand seven hundred and four – 4,07,704. (c) Fifty lakhs five thousand and fifty – 50,05,050. (d) Ten lakhs two hundred and thirty five – 10,02,035. Land of Tens
Textbook page 5 · solved item 14
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?
Show solution
(b) 10 times (because 10,000 ÷ 1000 = 10) (c) 53 times (because 53,000 ÷ 1000 = 53) (d) 90 times (because 90,000 ÷ 1000 = 90) (e) 100 times (because 1,00,000 ÷ 1000 = 100) (f) 1,53,000 (because 153 × 1000 = 1,53,000) (g) 1,00,000 ÷ 1000 = 100. Therefore, 100 thousands make one lakh.
Textbook page 5 · solved item 15
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
Show solution
(a) 50 times (because 500 ÷ 10 = 50) (b) 78 times (because 780 ÷ 10 = 78) (c) 100 times (because 1000 ÷ 10 = 100) (d) 370 times (because 3700 ÷ 10 = 370) (e) 1000 times (because 10,000 ÷ 10 = 1,000) (f) 10000 times (because 1,00,00 ÷ 10 = 10,000) (g) 4350 (because 435 × 10 = 4350)
Textbook page 5 · solved item 16
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.
Show solution
(a) 4 times (because 400 ÷ 100 = 4) (b) 37 times (because 3700 ÷ 100 = 37) (c) 100 times (because 10,000 ÷ 100 = 100) (d) 530 times (because 53,000 ÷ 100 = 530) (e) 900 times (because 90,000 ÷ 100 = 900) (f) 976 times (because 97,600 ÷ 100 = 976) (g) 1000 times (because 1,00,000 ÷ 100 = 1,000) (h) 58,200 (because 582 × 100 = 58,200) (i) 10,000 100 = 100 hundreds 100 hundreds make ten thousand.
(j) 1,00,000 100 = 1000 hundreds 1000 hundreds make one lakh. (k) Handy Hundreds' statement is true compared to Thoughtful Thousands because Thoughtful Thousands can’t show multiples of 100 or 10. However, Handy Hundreds' statement is false compared to Tedious Tens because Tedious Tens can reach any multiple of 100, although it would take many steps.
Complete worked answers
Textbook page 6
Textbook page 6 · solved item 17
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.
Show solution
First method: Press +10, 32 times → 32 × 10 = 320 Press +1 once → 1 On Adding, 320 + 1 = 321 Yes, Chitti reaches 321 this way. Second method: Press +100, 2 times → 2 × 100 = 200 Press +10, 12times → 12 × 10 = 120 Press +1 once → 1 On adding, 200 + 120 + 1 = 321 Again, Chitti reaches 321.
Textbook page 6 · solved item 18
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.
Show solution
(5 × 1000) + (0 × 100) + (7 × 10) + (2 × 1) = 5072. Figure it out
Textbook page 6 · solved item 19
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. (a) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813
Show solution
(a) 8300 (8 × 1000) + (3× 100) = 8300. (5 × 1000) + (30 × 100) + (30 × 10) = 8300. (b) 40629 (40 × 1000) + (6 × 100) + (2 × 10) + (9 × 1) = 40629 (35 × 1000) + (56 × 100) + (2 × 10) + (9 × 1) = 40629 (c) 56354 (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1) = 56354 (56 × 1000) + (3 × 100) + (5 × 10) + (4 × 1) = 56354 (d) 66666 (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1) = 66666 (66 × 1000) + (6 × 100) + (6 × 10) + (6 × 1) = 66666 (e) 367813 (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 1) = 367813 (30 × 10000) + (60 × 1000) + (70 × 100) + (81 × 10) + (3 ×1) = 367813
Complete worked answers
Textbook page 7
Textbook page 7 · solved item 20
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? (b) 997 can be made using 25 clicks. Can you make 997 with a different number of clicks?
Show solution
(a) Largest 3-digit number: (9 × 100) + (8 × 10) + (13 × 1) = 993 Total clicks = 9 + 8 + 13 = 30. Therefore, 993 is the largest 3-digit number made with 30 clicks. Smallest 3-digit number: (8 × 10) + (22 × 1) = 102 Total clicks = 8 + 22 = 30. Therefore, 102 is the smallest 3-digit number made with 30 clicks.
(b) (8 × 100) + (19 × 10) + (7 × 1) = 997. Total clicks = 8 + 19 + 7 = 34. Therefore, 997 can also be obtained in 34 clicks.
Textbook page 7 · solved item 21
Systematic Sippy is a different kind of calculator. It has the following buttons: +1, +10, +100, +1000, +10000, +100000. It wants to be used as minimally as possible. How can we get the numbers (a) 5072, (b) 8300 using as few button clicks as possible? Is there another way to get 5072 using less than 23 button clicks? Write the expression for the same.
Show solution
(a) 5072 (5 × 1,000) + (7 × 10) + (2 × 1) Total clicks = 5 + 7 + 2 = 14. Yes, 5072 can be obtained in 14 button clicks. (b) 8300 (8 × 1,000) + (3 × 100) Total clicks = 8 + 3 = 11. 8300 can be obtained in 11 button clicks.
Textbook page 7 · solved item 22
Is there another way to get 5072 using less than 23 button clicks? Write the expression for the same.
Show solution
(5 × 1,000) + (7 × 10) + (2 × 1) Total clicks = 5 + 7 + 2 = 14. Yes, 5072 can be obtained in less than 23 clicks i.e. 14 clicks. Figure it Out
Textbook page 7 · solved item 23
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. (a) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813
Show solution
(a) 8300 (8 × 1,000) + (3 × 100) = 8300 8300 can be obtained in 8+3 = 11 clicks. (b) 40629 (4 × 10,000) + (6 × 100) + (2 × 10) + (9 × 1) = 40629 40629 can be obtained in 4+6+2+9 = 21 clicks. (c) 56354 (5 × 10,000) + (6 × 1,000) + (3 × 100) + (5 × 10) + (4 × 1) = 56354 56354 can be obtained in 5+6+3+5+4 = 23 clicks.
(d) 66666 (6 × 10,000) + (6 × 1,000) + (6 × 100) + (6 × 10) + (6 × 1) = 66666 66666 can be obtained in 6+6+6+6+6 = 30 clicks. (e) 367813 (3 × 1,00,000) + (6 × 10,000) + (7 × 1,000) + (8 × 100) + (1 × 10) + (3 × 1) = 367813 367813 can be obtained in 3+6+7+8+1+3 = 28 clicks.
Textbook page 7 · solved item 24
2. Do you see any connection between each number and the corresponding smallest number of button clicks?
Show solution
The smallest number of button clicks for each number is the sum of its digits.
Textbook page 7 · solved item 25
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.
Show solution
The Indian place value system helps in identifying and differentiating between numbers easily by grouping them into thousands, lakhs, crores, etc..
Complete worked answers
Textbook page 8
Textbook page 8 · solved item 26
How many zeros does a thousand lakh have? _____
Show solution
Thousand lakh = 1,000 × 1,00,000 = 10,00,00,000 and it has 8 zeros.
Complete worked answers
Textbook page 9
Textbook page 9 · solved item 27
How many zeros does a hundred thousand have? ____
Show solution
Hundred thousand = 100 × 1,000 = 1,00,000 and it has 5 zeros. Figure it Out
Textbook page 9 · solved item 28
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
Show solution
(a) 40,50,678 Forty lakh fifty thousand six hundred and seventy-eight. Four million fifty thousand six hundred and seventy-eight. (b) 48121620 Four crore eighty-one lakh twenty-one thousand six hundred twenty. Forty-eight million one hundred twenty-one thousand six hundred twenty. (c) 20022002 Two crore twenty-two thousand and two.
Twenty million twenty-two thousand and two. (d) 246813579 Twenty four crore sixty eight lakh thirteen thousand five hundred and seventy nine. Two hundred forty-six million eight hundred thirteen thousand five hundred seventy nine. (e) 345000543 Thirty-four crore fifty lakh five hundred and forty-three.
Three hundred forty-five million five hundred forty-three. (f) 1020304050 One arab two crore three lakh four thousand and fifty. One billion, twenty million three hundred four thousand and fifty.
Textbook page 9 · solved item 29
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
Show solution
(a) 1,01,01,010. (b) 1,001,001,001. (c) 10,20,30,040. (d) 9,080,700,600.
Textbook page 9 · solved item 30
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
Show solution
(a) 30,000 < 3,00,000 Therefore, 30 thousand < 3 lakhs. (b) 5,00,00,000 > 5,000,000 Therefore, 500 lakhs > 5 million. (c) 8,00,000 < 5,000,000 Therefore, 800 thousand < 8 million. (d) 6,40,00,00,000 < 60,000,000,000 Therefore, 640 crore < 60 billion.
Complete worked answers
Textbook page 10
Textbook page 10 · solved item 31
Think and share situations where it is appropriate to (a) round up, (b) round down, (c) either rounding up or rounding down is okay and (d) when exact numbers are needed.
Show solution
(a) Round Up: Buying food for a group or occasion. Buying materials so you don’t run short. (b) Round Down: Shopkeeper saying lesser prices to attract buyers. Estimating fuel left to drive more carefully. Estimating remaining time to a meeting (e.g., saying 10 minutes left when it’s 12 minutes) to create urgency and avoid being late (c) Either is Okay: Casual talks.
Distance estimation between places. Telling academic results. (d) Exact Numbers Needed: Handling money (bank balance, salary, tax). Doing science experiments or engineering work. Dialling emergency numbers (like 100 for the police)
Complete worked answers
Textbook page 11
Textbook page 11 · solved item 32
Write the five nearest neighbours for these numbers: (a) 3,87,69,957 (b) 29,05,32,481
Show solution
(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
Textbook page 11 · solved item 33
I have a number for which all five nearest neighbours are 5,00,00,000. What could the number be? How many such numbers are there?
Show solution
A number between 4,99,99,500 and 5,00,00,499 (inclusive of the first, exclusive of the second) rounds to 5,00,00,000 at all five levels. There are 1000 such numbers. 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
Complete worked answers
Textbook page 13
Textbook page 13 · solved item 34
1. What is your general observation about this data? Share it with the class.
Show solution
1. Most cities have seen a significant rise in pollution from 2001 to 2011 with a few cities like Surat, Vadodara almost doubling their population. Some cities like Kolkata have shown very little growth.
Textbook page 13 · solved item 35
2. What is an appropriate title for the above table?
Show solution
2. Population of major Indian cities in 2001 and 2011.
Textbook page 13 · solved item 36
3. How much is the population of Pune in 2011? Approximately, by how much has it increased compared to 2001?
Show solution
3. Pune’s population in 2011 = 31,15,431. Pune’s population in 2001 = 25,38,473. Increase in population = 3,115,431 – 2,538,473 = 576,958. Approximately, the population increased by about 5.8 lakhs or nearly 6 lakhs.
Textbook page 13 · solved item 37
4. Which city’s population increased the most between 2001 and 2011?
Show solution
4. Population increase of some cities: Bengaluru: 84,25,970 - 43,01,326 = 41,24,644 Hyderabad: 68,09,970 - 36,37,483 = 31,72,487 Ahmedabad: 55,70,585 - 35,20,085 = 20,50,500 Surat: 44,67,797 - 24,33,835 = 20,33,962 Vadodara: 35,52,371 - 16,90,000 = 18,62,371 Bengaluru had the highest population increase: 41,24,644.
Textbook page 13 · solved item 38
5. Are there cities whose population has almost doubled? Which are they?
Show solution
5. Yes, several cities nearly doubled their population. They are: (i) Bengaluru 2001: 43,01,326 → 2011: 84,25,970 (ii) Hyderabad 2001: 36,37,483 → 2011: 68,09,970 (iii)Surat 2001: 24,33,835 → 2011: 44,67,797 (iv) Vadodara 2001: 16,90,000 → 2011: 35,52,371
Textbook page 13 · solved item 39
6. By what number should we multiply Patna’s population to get a number/population close to that of Mumbai?
Show solution
6. Mumbai (2011): 1,24,42,373 Patna (2011): 16,84,222 Multiplier = 1,24,42,373 16,84,222 =7.39 Therefore, we should multiply Patna’s population by 7.39 to get a number close to that of Mumbai.
Complete worked answers
Textbook page 14
Textbook page 14 · solved item 40
Using the meaning of multiplication and division, can you explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10?
Show solution
Multiplying by 5 is the same as multiplying by 10 and then dividing by 2 because 10 2 = 10 ÷ 2 2 ÷ 2 = 5. Figure it out
Textbook page 14 · solved item 41
1. Find quick ways to calculate these products: (a) 2 × 1768 × 50 (b) 72 × 125 [Hint: 125 = 1000 8 ] (c) 125 × 40 × 8 × 25
Show solution
(a) 2 × 1768 × 50 = 2 × 50 × 1768 = 100 × 1768 = 17680. (b) 72 × 125 = 72 × 1000 8 = 9 × 1000 = 9000. (c) 125 × 40 × 8 × 25 = 125 × 8 × 40 × 25 = 1000 × 1000 = 10,00,000.
Textbook page 14 · solved item 42
2. Calculate these products quickly. (a) 25 × 12 = _____________ (b) 25 × 240 = _____________ (c) 250 × 120 = _____________ (d) 2500 × 12 =_____________ (e) ______×______= 120000000
Show solution
(a) 25 × 12 = 100 4 × 12 = 100 × 3 = 300. (b) 25 × 240 = 100 4 × 240 = 100 × 60 = 6000. (c) 250 × 120 = 1,000 4 × 120 = 1000 × 30 = 30000. (d) 2500 × 12 = 10,000 4 × 12 = 10,000 × 3 = 30,000. (e) 4800 × 25000 = 12,00,00,000 4800 × 1,00,000 4 = 12,00,00,000 1200 × 1,00,000 = 12,00,00,000.
Textbook page 14 · solved item 43
In each of the following boxes, the multiplications produce interesting patterns. Evaluate them to find the pattern. Extend the multiplications based on the observed pattern.
Show solution
11 × 11 = 121 111 × 111 = 12321 1111 × 1111 = 1234321 11111 × 11111 = 123454321 66 × 61 = 4026 666 × 661 = 440226 6666 × 6661 = 44402226 66666 × 66661 = 4444022226 3 × 5 = 15 33 × 35 = 1155 333 × 335 = 111555 3333 × 3335 = 11115555 101 × 101 = 10201 102 × 102 = 10404 103 × 103 = 10609 104 × 104 = 10816
Complete worked answers
Textbook page 15
Textbook page 15 · solved item 44
Observe the number of digits in the two numbers being multiplied and their product in each case. Is there any connection between the numbers being multiplied and the number of digits in their product?
Show solution
The number of digits in the product becomes twice, one less than twice, or one more than twice compared to the number of digits in the in the multiplied numbers.
Textbook page 15 · solved item 45
Roxie says that the product of two 2-digit numbers can only be a 3- or a 4-digit number. Is she correct?
Show solution
Yes, she is correct. Because, product of smallest two 2-digit numbers = 10 × 10 = 100 (3-digit number) And the product of the largest two 3-digit numbers = 99 × 99 = 9801 (4-digit number).
Textbook page 15 · solved item 46
Should we try all possible multiplications with 2-digit numbers to tell whether Roxie’s claim is true? Or is there a better way to find out?
Show solution
No, we don’t need to do all possible multiplications, check extremes: 10×10 and 99×99 give the minimum and maximum digits possible.
Textbook page 15 · solved item 47
Can multiplying a 3-digit number with another 3-digit number give a 4-digit number?
Show solution
Product of smallest two 3-digit numbers = 100 × 100 = 10,000 (4-digit number) Product of largest two 3-digit numbers = 999 × 999 = 9,98,001 (5-digit number) Therefore, a 4-digit number can’t be obtained by multiplying two 3-digit numbers.
Textbook page 15 · solved item 48
Can multiplying a 4-digit number with a 2-digit number give a 5-digit number?
Show solution
Product of smallest 4-difit number and a 2-digit number = 1,000 × 10 = 10,000 (4-digit number) Product of largest 4-digit number and a 2-digit number = 9,999 × 99 = 9,89,901 (5-digit number) Yes, it is possible.
Textbook page 15 · solved item 49
Observe the multiplication statements below. Do you notice any patterns? See if this pattern extends for other numbers as well.
Show solution
1×1-digit = 1 or 2 digits 2×1-digit = 2 or 3 digits 2×2-digit = 3 or 4 digits 3×3-digit = 5 or 6 digits 5×5-digit = 9–10 digits (Min = 5+5–1, Max = 5+5) 8×3-digit = 10–11 digits (Min = 8+3–1, Max = 8+3) 12×13-digit = 24–25 digits (Min = 12+13–1, Max = 12+13)
Complete worked answers
Textbook page 16
Textbook page 16 · solved item 50
1250 × 380 _____ is the number of kīrtanas composed by Purandaradāsa according to legends.
Show solution
Kirtanas = 1250 × 380 = (125 × 10) × (38 × 10) = 125 × 38 × 10 × 10 = 4,750 × 100 = 4,75,000.
Textbook page 16 · solved item 51
2100 × 70,000 _____ is the approximate distance in kilometers, between the Earth and the Sun.
Show solution
Distance = 2100 × 70,000 = (21 × 1,000) × (7 × 10,000) = 21 × 7 × 1,000 × 10,000 = 147 × 1,00,00,000 = 1,47,00,00,000 km
Complete worked answers
Textbook page 17
Textbook page 17 · solved item 52
6400 × 62,500 _____ is the average number of litres of water the Amazon river discharges into the Atlantic Ocean every second.
Show solution
Average = 6,400 × 62,500 = (64 × 100) × (625 × 100) = 64 × 625 × 100× 100 = 40,000 × 10,000 = 40,00,00,000 litres.
Textbook page 17 · solved item 53
13,95,000 ÷ 150 ____ is the distance (in kms) of the longest single-train journey in the world.
Show solution
Distance = 13,95,000 150 = 9300 km.
Complete worked answers
Textbook page 18
Textbook page 18 · solved item 54
Adult blue whales can weigh more than 10,50,00,000 ÷ 700 ___ kilograms.
Show solution
Weight = 10,50,00,000 700 = 1,50,000 kg.
Textbook page 18 · solved item 55
52,00,00,00,000 ÷ 130 ___ was the weight, in tonnes, of global plastic waste generated in the year 2021.
Show solution
Weight (in tonnes) = 52,00,00,00,000 130 = 40,00,00,000.
Complete worked answers
Textbook page 19
Textbook page 19 · solved item 56
The RMS Titanic ship carried about 2500 passengers. Can the population of Mumbai fit into 5000 such ships?
Show solution
Passengers in one ship = 2500 Passengers in 5000 ships = 5000 × 2500 = 1,25,00,000. Population of Mumbai = 1,24,00,00 Therefore, the population of Mumbai can easily fit into 500 such ships.
Textbook page 19 · solved item 57
Find out if you can reach the Sun in a lifetime, if you travel 1000 kilometers every day. (Distance between the Sun and the Earth from calculation = 147,000,000 km)
Show solution
Distance between the Sun and the Earth = 14,70,00,000 km Distance travelled in one day = 1000 km Distance travelled in one year (365 days) = 365 × 1000 = 3,65,000 km Time (in years) to reach the Sun = 14,70,00,000 3,65,000 = 403 years Since a man can’t live up to 403 years. So, you can’t reach the Sun in a lifetime.
Textbook page 19 · solved item 58
Make necessary reasonable assumptions and answer the questions below: (a) If a single sheet of paper weighs 5 grams, could you lift one lakh sheets of paper together at the same time? (b) If 250 babies are born every minute across the world, will a million babies be born in a day? (c) Can you count 1 million coins in a day? Assume you can count 1 coin every second.
Show solution
(a) Weight of single sheet = 5 grams Weight of 1 lakh sheets = 1,00,000 × 5 = 5,00,000 grams = 5,00,000 1000 = 500 kg. Since, a typical person can’t lift 500 kg. Therefore, you couldn’t lift one lakh sheets of paper. (b) Babies born in a minute = 250 babies Babies born in an hour = 250 × 60 = 15,000 babies Babies born in a day = 15,000 × 24 = 3,60,000 babies Since, 3,60,000 is less than 1 million (10 lakh).
Therefore, a million babies will not be born in a year. (c) Coins counted per sec = 1 coin Coins counted per minute = 60 coins Coins counted per hour = 60 × 60 = 3,600 coins Coins counted per day = 3,600 × 24 = 86,400 coins Since, 84,000 is much less than 1 million (10 lakh). Therefore, you can’t count 1 million coins in a day.
Figure it out
Textbook page 19 · solved item 59
1. Using all digits from 0 – 9 exactly once (the first digit cannot be 0) to create a 10-digit number, write the — (a) Largest multiple of 5 (b) Smallest even number
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(a) Arranging digits in decreasing order = 9,8,7,6,5,4,3,2,1,0 All multiples of 5 can end only in 5 or 0. Therefore, Largest multiple of 5 = 9876543210. (b) Arranging digits in ascending order = 0,1,2,3,4,5,6,7,8,9 Since, number can’t start with zero. So, the smallest number = 1023456789 Swapping the last two digits to make the above number even.
Therefore, Smallest even number = 1023456798.
Complete worked answers
Textbook page 20
Textbook page 20 · solved item 60
2. The number 10,30,285 in words is Ten lakhs thirty thousand two hundred eighty five, which has 43 letters. Give a 7-digit number name which has the maximum number of letters.
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Using 7 and 8 to make such a number since both numbers contain 5 letters when written in words. 77,77,777 = Seventy-seven lakh seventy-seven thousand seven hundred seventy-seven. Letters in 77,77,777 = 60. 88,88,888 = Eighty-eight lakh eighty-eight thousand eight hundred eighty-eight. Letters in 88,88,888 = 57.
Therefore, 77,77,777 has the maximum number of letters in its number name.
Textbook page 20 · solved item 61
3. Write a 9-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?
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A 9-digit number where exchanging any two digits results in a bigger number = 987654321. Only one such number exists.
Textbook page 20 · solved item 62
4. Strike out 10 digits from the number 12345123451234512345 so that the remaining number is as large as possible.
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Striking out smaller numbers 1,2,3,4 from the given number, we get 5534512345.
Textbook page 20 · solved item 63
5. The words ‘zero’ and ‘one’ share letters ‘e’ and ‘o’. The words ‘one’ and ‘two’ share a letter ‘o’, and the words ‘two’ and ‘three’ also share a letter ‘t’. How far do you have to count to find two consecutive numbers which do not share an English letter in common?
Show solution
Let’s check: Let’s check: one & two share o two & three share t, e three & four share r four & five share f five & six share i six & seven share s seven & eight share e eight & nine share e, i, n nine & ten share n, e It shows that all consecutive numbers have at least one common letter. So, there is no such pair of consecutive numbers that do not share an English letter in common.
Textbook page 20 · solved item 64
6. Suppose you write down all the numbers 1, 2, 3, 4, ..., 9, 10, 11, ... The tenth digit you write is ‘1’ and the eleventh digit is ‘0’, as part of the number 10. (a) What would the 1000th digit be? At which number would it occur? (b) What number would contain the millionth digit? (c) When would you have written the digit ‘5’ for the 5000th time?
Show solution
(a) Digits from 1 to9 = 9 digits Digits from 10 to 99 = 90 numbers × 2 = 180 digits Total digits from 1 to 99 = 189 digits Remaining digits to reach 1000th digit = 1000 – 189 = 811 Numbers with 3 3-digit numbers = 811/3 = 270 full numbers + 1 digit left over. The first 3-digit number is 100 270th 3 digit number is 100 + 270 – 1 = 369 The next number is 370.
The first digit of 370, which is 3, is the 1000th digit.
Textbook page 20 · solved item 65
7. A calculator has only ‘+10,000’ and ‘+100’ buttons. Write an expression describing the number of button clicks to be made for the following numbers: (a) 20,800 (b) 92,100 (c) 1,20,500 (d) 65,30,000 (e) 70,25,700
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(a) 20,800 = (2 × 10,000) + (8 × 100) Total clicks = 2 + 8 = 10 clicks. (b) 92,100 = (9 × 10,000) + (21 × 100) Total clicks = 9 + 21 = 30 clicks. (c) 1,20,000 = (12 × 10,000) Total clicks = 12 clicks. (d) 65,30,000 = (653 × 10,000) Total clicks = 653 clicks. (e) 70,25,700 = (702 × 10,000) + (57 × 100) Total clicks = 759 clicks.
Textbook page 20 · solved item 66
8. How many lakhs make a billion?
Show solution
1 lakh = 1,00,000 1 billion = 1,000,000,000 Number of lakhs making a billion = 1,000,000,000 1,00,000 = 10,000.
Textbook page 20 · solved item 67
9. You are given two sets of number cards numbered from 1 – 9. Place a number card in each box below to get the (a) largest possible sum (b) smallest possible difference of the two resulting numbers.
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(a) 9 8 7 6 5 4 3 9 8 7 6 5 To get the largest possible sum, both the 7-digit and 5-digit numbers need to be the largest. 7-digit number = 98,76,543 5-digit number = 98,765 Sum = 98,76,543 + 98,765 = 99,75,308. (b) To get the smallest possible difference, the 7-digit number needs to be the smallest and the 5-digit number needs to be the largest.
7-digit number = 12,34,567 5-digit number = 98,765 Difference = 12,34,567 – 98,765 = 11,35,802
Complete worked answers
Textbook page 21
Textbook page 21 · solved item 68
10. You are given some number cards; 4000, 13000, 300, 70000, 150000, 20, 5. Using the cards get as close as you can to the numbers below using any operation you want. Each card can be used only once for making a particular number. (a) 1,10,000: Closest I could make is 4000 × (20 + 5) + 13000 = 1,13,000 (b) 2,00,000: (c) 5,80,000: (d) 12,45,000: (e) 20,90,800:
Show solution
(a) 1,10,000: Closest estimate = 70,000 + (4,000 × 5) + 13,000 = 1,03,000. (b) 2,00,000: Closest estimate = 1,50,000 + 70,000 – (4,000 × 5) = 2,00,000. (c) 5,80,000: Closest estimate = (1,50,000 × 4) – (4000 × 5) = 5,80,000. (d) 12,45,000: Closest estimate = (1,50,000 × 8) + (13,000 × 4) – 4,000 = 12,48,000.
(e) 20,90,800: Closest estimate = (1,50,000 × 14) + 4000 – 13000 = 20,91,000.
Textbook page 21 · solved item 69
11. Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each coin is 1 mm thick. 1 2 3 4 5 6 7 9 8 7 6 5
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Height of each coin = 1 mm Height of Statue of Unity = 180 m = 180 × 100 × 10 mm = 1,80,000 mm. Number of coins to be stacked = 1,80,000 mm 1 mm = 1,80,000 coins.
Textbook page 21 · solved item 70
12. Grey-headed albatrosses have a roughly 7-feet wide wingspan. They are known to migrate across several oceans. Albatrosses can cover about 900 – 1000 km in a day. One of the longest single trips recorded is about 12,000 km. How many days would such a trip take to cross the Pacific Ocean approximately?
Show solution
Total trip = 12,000 km Distance covered in a day = 900 – 1000 km Estimated Number of days if it flies 900 km/day = 12,000 900 = 13.3 days Estimated Number of days if it flies 1000 km/day = 12,000 1,000 = 12 days Therefore, It would take approximately 12 to 14 days for a grey-headed albatross to complete a 12,000 km trip across the Pacific Ocean.
Textbook page 21 · solved item 71
13. A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled 13,560 km from Alaska to Australia without stopping. Its journey started on 13 October 2022 and continued for about 11 days. Find out the approximate distance it covered every day. Find out the approximate distance it covered every hour.
Show solution
Total distance = 13,560 km Duration = 11 days Each day = 24 hours Duration in hours = 11 × 24 = 264 hours Distance covered per day = 13,560 km 11 days = 1232.73 km or 1233 km. Distance covered per hour = 13,560 km 264 hours = 51.36 km or 51 km.
Textbook page 21 · solved item 72
14. Bald eagles are known to fly as high as 4500 – 6000 m above the ground level. Mount Everest is about 8850 m high. Aeroplanes can fly as high as 10,000 – 12,800 m. How many times bigger are these heights compared to Somu’s building?
Show solution
Height of Somu’s building = 40 m (i) Bald eagles’ flight height = 4500 – 6000 m • Lower estimate = 4500 40 = 112.5 • Upper estimate = 6000 40 = 150 Therefore, Bald eagles fly about 112 to 150 times higher than Somu’s building. (ii) Mount Everest height = 8850 m 8850 40 = 221.25 Therefore, Mount Everest is about 221 times taller than Somu’s building.
(iii) Aeroplanes flight height = 10,000 – 12,000 m • Lower estimate = 10,000 40 = 250 • Upper estimate = 12,000 40 = 320 Therefore, Airplanes fly about 250 to 320 times higher than Somu’s building.