Large Numbers Around Us

Calculate the product to uncover the fact. Once you find the product, read the number in both Indian and American naming systems. Share your thoughts and questions about the fact with the class after you discover each number.

As you did before, divide the given numbers to uncover interesting facts about division. Share your thoughts and questions with the class after you uncover each number.

Share such large-number facts you know / come across with your class.

To make the digit 7, three sticks are needed.

Write or make the number 5108. How many sticks are required?

1. Make or write the number 42,019. It would require exactly 23 sticks.

2. Starting with 42,019, add or write two more sticks, and make a bigger number. One example is 42,078. What other numbers bigger than 42,019 can you make in this way?

3. Preetham wants to insert the digit '1' somewhere among the digits '4', '2', '0', '1' and '9'. Where should he place the digit '1' to get the biggest possible number?

4. What other numbers can he make by placing the digit '1'?

1. Make or write the number 63,890.

2. Starting with 63,890, rearrange exactly four sticks and make a bigger number. One example is 88,078. What other numbers bigger than 63,890 can you make in this way?

1. Make any number using exactly 24 sticks or lines.

2. What is the biggest number that can be made using 24 sticks or lines?

3. What is the smallest number that can be made using 24 sticks or lines?

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?

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

By how much did the population of Chintamani increase from 2011 to 2024?

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

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.

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

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.

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

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

Compare and write '<', '>' or '=':

(a) 30 thousand ______ 3 lakhs

(b) 500 lakhs ______ 5 million

(c) 800 thousand ______ 8 million

(d) 640 crore ______ 60 billion

Find quick ways to calculate these products:

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

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

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

Calculate these products quickly.

(a) $25 \times 12 =$ _______

(b) $25 \times 240 =$ _______

(c) $250 \times 120 =$ _______

(d) $2500 \times 12 =$ _______

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

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

The number 10,30,285 in words is Ten lakhs thirty thousand two hundred eighty five, which has 42 letters. Give a 7-digit number name which has the maximum number of letters.

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

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

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?

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?

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

How many lakhs make a billion?

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.

You are given some number cards; 4000, 13000, 3000, 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:

Find out how many coins should be stacked to match the height of the Statue of Unity. Assume each coin is 1 mm thick.

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?

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.

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?

Estu was surprised to know that there were about one lakh varieties of rice in this country. He wondered “One lakh! So far I have only tasted 3 varieties. If we tried a new variety each day, would we even come close to tasting all the varieties in a lifetime of 100 years?”

What do you think? Guess.

But how much is one lakh? Observe the pattern and fill in the boxes given below.

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.

Context: If we ignore leap years, there are 365 days in a year. For $y$ years, the number of days is $365 \times y$.

Q. Choose a number for $y$. How close to one lakh is the number of days in $y$ years, for the $y$ of your choice?

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?

Context: The world's tallest statue is the 'Statue of Unity' in Gujarat depicting Sardar Vallabhbhai Patel. Its height is about 180 metres. Somu is 1 metre tall. If each floor of the building is about four times his height, the approximate height of the building is 40 metres.

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

__________ m.

Context: Kunchikal waterfall in Karnataka is said to drop from a height of about 450 metres. Somu is 1 metre tall. If each floor of the building is about four times his height, the approximate height of the building is 40 metres.

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

__________ m.

Context: Kunchikal waterfall in Karnataka is said to drop from a height of about 450 metres. Somu is 1 metre tall. If each floor of the building is about four times his height, the approximate height of the building is 40 metres.

Q. How many floors should Somu's building have to be as high as the waterfall?

__________ .

How do you view a lakh — is a lakh big or small?

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

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

1. The Thoughtful Thousands only has a $+1000$ button. How many times should it be pressed to show:

(a) $4000$

(b) $7000$

(c) $10,000$

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

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.

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.

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

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

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?

Create questions like these and challenge your classmates.

How can we get the numbers (a) 5072, (b) 8300 using as few button clicks as possible?

Find out which buttons should be clicked and how many times to get the desired numbers given in the table. The aim is to click as few buttons as possible.

Here is one way to get the number 5072. This method uses 23 button clicks in total. Is there another way to get 5072 using less than 23 button clicks? Write the expression for the same.

How many zeros does a thousand lakh have?

How many zeros does a hundred thousand have?

What do you think of this conversation? Have you read or heard such headlines or statements?

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.

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?

Roxie and Estu are estimating the values of simple expressions.

1. 4,63,128 + 4,19,682,

Roxie: “The sum is near 8,00,000 and is more than 8,00,000.” Estu: “The sum is near 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 = ________

14,63,128 – 4,90,020

Roxie: “The difference is near 10,00,000 and is less than 10,00,000.” Estu: “The difference is near 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 = ________

From the information given in the table, answer the following questions by approximation:

(i) What is your general observation about this data? Share it with the class.

(ii) What is an appropriate title for the above table?

(iii) How much is the population of Pune in 2011? Approximately, by how much has it increased compared to 2001?

(iv) Which city's population increased the most between 2001 and 2011?

(v) Are there cities whose population has almost doubled? Which are they?

(vi) By what number should we multiply Patna's population to get a number/population close to that of Mumbai?

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?

How Long is the Product?

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.

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?

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

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?

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

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

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

Calculate the product to uncover the fact:

$1250 \times 380$

Read the resulting number in both Indian and American naming systems.

Also consider the questions:

• How many years did he live to compose so many songs?
• At what age did he start composing songs?
• If he composed 4,75,000 songs, how many songs per year did he have to compose?

Calculate the product to uncover the fact:

$2100 \times 70,000$

Read the resulting number in both Indian and American naming systems.

Calculate the quotient to uncover the fact:

$10,50,00,000 \div 700$

Calculate the quotient to uncover the fact:

$52,00,00,000,000 \div 130$

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

Inspired by this strange question, Roxie wondered, “If I could travel 100 kilometers every day, could I reach the Moon in 10 years?” (The distance between the Earth and the Moon is 3,84,400 km.)

• How far would she have travelled in a year?
• How far would she have travelled in 10 years?
• Is it not easier to perform these calculations in stages? You can use this method for all large calculations.

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.)

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.

Think and create more such fun questions and share them with your class.