Chapter 1 Large Numbers Around Us (Class 7 - Latest Maths NCERT (Ganita Prakash I) Solutions)

Question. Observe the pattern and fill in the boxes given below.

Question 1. According to the $2011$ Census, the population of the town of Chintamani was about $75,000$. How much less than one lakh is $75,000$?

Question 2. The estimated population of Chintamani in the year $2024$ is $1,06,000$. How much more than one lakh is $1,06,000$?

Question 3. By how much did the population of Chintamani increase from $2011$ to $2024$?

Question 1. Which is taller — The Statue of Unity or this building? How much taller?

Question 2. We can see that the height of the Statue of Unity is close to $4$ times the height of Somu’s building.

How much taller is the Kunchikal waterfall than Somu's building?

Question 3. How many floors should Somu’s building have to be as high as the waterfall?

Question. Write each of the numbers given below in words:

(a) $3,00,600$

(b) $5,04,085$

(c) $27,30,000$

(d) $70,53,138$

Question. 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

Question 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?

Question 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

Question 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.

Question 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.

Find a different way to get $5072$ and write an expression for the same.

Question. 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) $367813$

Question. 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?

Question. 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 using as few button clicks as possible?

(a) $5072$

(b) $8300$

Question 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.

Question 2. Do you see any connection between each number and the corresponding smallest number of button clicks?

Question 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.

Question. How many zeros does a thousand lakh have? _____

Question. How many zeros does a hundred thousand have? ____

Question 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) $1020304050$

Question 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

Question 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

Question 1. Think and share situations where it is appropriate to:

(a) round up

(b) round down

(c) either rounding up or rounding down is okay

(d) when exact numbers are needed

Question 1. With large numbers it is useful to know the nearest thousand, lakh or crore. For example, the nearest neighbours of the number $6,72,85,183$ are shown in the table below.

Similarly, write the five nearest neighbours for these numbers:

(a) $3,87,69,957$

(b) $29,05,32,481$

Question 2. 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?

Question. From the information given in the table, answer the following question by approximation:

1. What is your general observation about this data? Share it with the class.

2. What is an appropriate title for the above table?

3. How much is the population of Pune in $2011$? Approximately, by how much has it increased compared to $2001$?

4. Which city’s population increased the most between $2001$ and $2011$?

5. Are there cities whose population has almost doubled? Which are they?

6. By what number should we multiply Patna’s population to get a number/population close to that of Mumbai?

Question. Using the meaning of multiplication and division, can you explain why multiplying by $5$ is the same as dividing by $2$ and multiplying by $10$?

Question 1. Find quick ways to calculate these products:

(a) $2 \times 1768 \times 50$

(b) $72 \times 125$ [Hint: $125 = \frac{1000}{8}$]

(c) $125 \times 40 \times 8 \times 25$

Question 2. Calculate these products quickly.

(a) $25 \times 12 = $ _____________

(b) $25 \times 240 = $ _____________

(c) $250 \times 120 = $ _____________

(d) $2500 \times 12 = $ _____________

(e) ______ $\times$ ______ $= 120000000$

Question. 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?

Question. Roxie says that the product of two $2$-digit numbers can only be a $3$- or a $4$-digit number. Is she correct?

Question. 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?

She explains her reasoning: “We want to know about the number of digits in the product of two $2$-digit numbers. To know the smallest such product I took $10 \times 10$, so all other products will be greater than $100$. To know the greatest such product I multiplied the smallest $3$-digit numbers ($100 \times 100$) to get $10,000$; so the product of all the $2$-digit multiplications will be less than $10,000$.”

Question. Can multiplying a $3$-digit number with another $3$-digit number give a $4$-digit number?

Question. Can multiplying a $4$-digit number with a $2$-digit number give a $5$-digit number?

Question. Observe the multiplication statements below. Do you notice any patterns? See if this pattern extends for other numbers as well.

Question. The RMS Titanic ship carried about $2500$ passengers. Can the population of Mumbai fit into $5000$ such ships?

The population of Mumbai is more than $1$ crore $24$ lakhs.

Question. Find out if you can reach the Sun in a lifetime, if you travel $1000$ kilometers every day. (You had written down the distance between the Earth and the Sun in a previous exercise.)

Question. 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.

Question 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

Question 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.

Question 3. Write a $9$-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?

Question 4. Strike out $10$ digits from the number $12345123451234512345$ so that the remaining number is as large as possible.

Question 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?

Question 6. Suppose you write down all the numbers $1, 2, 3, 4, \dots, 9, 10, 11, \dots$ The $10^{th}$ digit you write is ‘$1$’ and the $11^{th}$ digit is ‘$0$’, as part of the number $10$.

(a) What would the $1000^{th}$ 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 $5000^{th}$ time?

Question 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) $70,25,700$

Question 8. How many lakhs make a billion?

Question 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.

Question 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 $4000 \times (20 + 5) + 13000 = 1,13,000$

(b) $2,00,000$:

(c) $5,80,000$:

(d) $12,45,000$:

(e) $20,90,800$:

Question 11. Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each coin is $1 \text{ mm}$ thick.

Question 12. Grey-headed albatrosses have a roughly $7$-feet wide wingspan. They are known to migrate across several oceans. Albatrosses can cover about $900 - 1000 \text{ km}$ in a day. One of the longest single trips recorded is about $12,000 \text{ km}$. How many days would such a trip take to cross the Pacific Ocean approximately?

Question 13. A bar-tailed godwit holds the record for the longest recorded non-stop flight. It travelled $13,560 \text{ km}$ from Alaska to Australia without stopping. Its journey started on $13 \text{ October } 2022$ and continued for about $11 \text{ days}$. Find out the approximate distance it covered every day. Find out the approximate distance it covered every hour.

Question 14. Bald eagles are known to fly as high as $4500 - 6000 \text{ m}$ above the ground level. Mount Everest is about $8850 \text{ m}$ high. Aeroplanes can fly as high as $10,000 - 12,800 \text{ m}$. How many times bigger are these heights compared to Somu’s building?