Class 7 Mathematics

Chapter 1 Solutions — Large Numbers Around Us

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Solutions

Overview

Step-by-step NCERT solutions for Large Numbers Around Us (Chapter 1, NCERT Class 7 Mathematics) — the full working for every question, not just the final answer. You can also read the Large Numbers Around Us textbook chapter.

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What these solutions cover

All 44 questions in Large Numbers Around Us are solved in the PDF. Here's what's inside, exercise by exercise:

A Lakh Varieties!

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?

Land of Tens

1.
The Thoughtful Thousands only has a +1000 button. How many times should it be pressed to show:
- (a) Three thousand?
- (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?
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?
- (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…

Creative Chitti — Different Ways to Express Numbers

1.
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
2.
Creative Chitti questions:
- (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?

Systematic Sippy — Minimum Button Clicks

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?

Of Crores and Crores! — Indian and American Number Systems

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
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
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

Exact and Approximate Values — Nearest Neighbours

1.
Similarly, write the five nearest neighbours for these numbers:
- (a) 3,87,69,957
- (b) 29,05,32,481
2.
Roxie and Estu are estimating: 4,63,128 + 4,19,682. Roxie says: 'The sum is near 8,00,000 and is more than 8,00,000.' Estu says: 'The sum is near 9,00,000 and is less than 9,00,000.'
- (a) Are these estimates correct? Whose is closer?
- (b) Will the sum be greater than 8,50,000 or less?
- (c) Will the sum be greater than 8,83,128 or less?
- (d) Exact value of 4,63,128 + 4,19,682 = ?
3.
Estimating: 14,63,128 – 4,90,020. Roxie says: 'The difference is near 10,00,000 and is less than 10,00,000.' Estu says: 'The difference is near 9,00,000 and is more than 9,00,000.'
- (a) Are these estimates correct? Whose is closer?
- (b) Will the difference be greater than 9,50,000 or less?
- (c) Will the difference be greater than 9,63,128 or less?
- (d) Exact value of 14,63,128 – 4,90,020 = ?

Populations of Cities

What is your general observation about the population data of Indian cities (2001 and 2011)? Share it with the class.
What is an appropriate title for the above table?
How much is the population of Pune in 2011? Approximately, by how much has it increased compared to 2001?
Which city's population increased the most between 2001 and 2011?
Are there cities whose population has almost doubled? Which are they?
By what number should we multiply Patna's population to get a number/population close to that of Mumbai?

Patterns in Products — Quick Multiplication

1.
Find quick ways to calculate these products:
- (a) 2 × 1768 × 50
- (b) 72 × 125 [Hint: 125 = 1000/8]
- (c) 125 × 40 × 8 × 25
2.
Calculate these products quickly:
- (a) 25 × 12
- (b) 25 × 240
- (c) 250 × 120
- (d) 2500 × 12
- (e) _____ × _____ = 12,00,00,000

Fascinating Facts about Large Numbers

Calculate the product to uncover the fact: 1250 × 380 = _____ is the number of kīrtanas composed by Purandaradāsa according to legends. Read the number in both Indian and American naming systems.
Calculate the product: 2100 × 70,000 = _____ is the approximate distance in kilometres between the Earth and the Sun. Read in both systems.
Calculate the product: 6400 × 62,500 = _____ is the average number of litres of water the Amazon river discharges into the Atlantic Ocean every second. Read in both systems.
Calculate the quotient: 13,95,000 ÷ 150 = _____ is the distance in km of the longest single-train journey in the world (Moscow to Vladivostok). Read in both systems.
Calculate the quotient: 10,50,00,000 ÷ 700 = _____ kilograms. Adult blue whales can weigh more than this. Read in both systems.
Calculate the quotient: 52,00,00,00,000 ÷ 130 = _____ was the weight in tonnes of global plastic waste in 2021. Read in both systems.

Did You Ever Wonder…? — Large Number Puzzles

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
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 '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?
6.
Suppose you write down all the numbers 1, 2, 3, 4, …, 9, 10, 11, ... The 10th digit you write is '1' and the 11th digit is '0' (part of 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?
7.
A calculator has only '+10,000' and '+100' buttons. Write an expression describing the number of button clicks for:
- (a) 20,800
- (b) 92,100
- (c) 1,20,500
- (d) 65,30,000
- (e) 70,25,700
How many lakhs make a billion?
9.
You are given two sets of number cards numbered from 1–9. Place a number card in each box to get the
- (a) largest possible sum
- (b) smallest possible difference of the two resulting numbers. (There are 7 boxes in the top row and 5 boxes in the bottom row.)
10.
You are given number cards: 4000, 13000, 300, 70000, 150000, 20, 5. Using the cards, get as close as you can to:
- (a) 1,10,000
- (b) 2,00,000
- (c) 5,80,000
- (d) 12,45,000
- (e) 20,90,800. Each card can be used only once.
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 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 travelled 13,560 km from Alaska to Australia without stopping, in about 11 days. Find the approximate distance it covered every day and every hour.
Bald eagles fly as high as 4500–6000 m. 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? (Somu's building is 10 floors × 4 m/floor = 40 m.)

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