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NCERT Solutions · Maths Ch 1
Large Numbers Around Us
43 questions · 6 exercises
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Ex 1.1
Ex 1.2
Ex 1.3
Ex 1.4
Ex 1.5
Ex 1.6
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 1.1 · 4 QUESTIONS
Getting a Feel of Large Numbers
Q1
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?
(2 marks)
Q2
The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?
(1 mark)
Q3
By how much did the population of Chintamani increase from 2011 to 2024?
(2 marks)
Q4
Somu is 1 metre tall. Each floor of the building is about four times his height. The building has 10 floors (picture). (i) What is the approximate height of the building? (ii) The Statue of Unity is 180 m tall. Which is taller, the statue or the building, and by how much? (iii) The Kunchikal waterfall drops from about 450 m. How much taller is it than Somu's building? (iv) How many floors should Somu's building have to be as high as the waterfall?
(3 marks)
2
EXERCISE 1.2 · 11 QUESTIONS
Reading and Writing Large Numbers
Q5
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
(3 marks)
Q6
Write the corresponding number 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
(3 marks)
Q7
Thoughtful Thousand counts in thousands. How many times must he count 1000 to make: (a) 3000 (b) 10,000 (c) 53,000 (d) 90,000 (e) 1 lakh (f) 1,53,000 (g) How many thousands make one lakh?
(3 marks)
Q8
Tedious Tens counts in tens. How many times must he count 10 to make: (a) 500 (b) 780 (c) 1000 (d) 3700 (e) 10,000 (f) one lakh (g) 4350
(3 marks)
Q9
Handy Hundreds counts in hundreds. How many times must he count 100 to make: (a) 400 (b) 3700 (c) 10,000 (d) 53,000 (e) 90,000 (f) 97,600 (g) 1,00,000 (h) 58,200? (i) How many hundreds make ten thousand? (j) How many hundreds 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 true?
(5 marks)
Q10
Chitti's calculator has buttons +1, +10, +100, +1000, +10000, +100000. The number 5072 can be shown as (5 × 1000) + (7 × 10) + (2 × 1). Find a different way to get 5072 and write an expression for it.
(2 marks)
Q11
For each number below write expressions for at least two different ways to obtain the number through button clicks: (a) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813
(5 marks)
Q12
Creative Chitti has some 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?
(5 marks)
Q13
Systematic Sippy wants to use as few clicks as possible. How can we get (a) 5072 and (b) 8300 with the fewest button clicks? Write the expressions.
(2 marks)
Q14
Find the smallest number of clicks for each number and write the expression: (a) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813. Do you see any connection between each number and its smallest number of button clicks? Why do the expressions also give the Indian place value notation?
(5 marks)
Q15
How many zeroes does a thousand lakh have? How many zeroes does a hundred thousand have?
(2 marks)
3
EXERCISE 1.3 · 3 QUESTIONS
Of Crores and Crores
Q16
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
(3 marks)
Q17
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 marks)
Q18
Compare and write '' or '=': (a) 30 thousand __ 3 lakhs (b) 500 lakhs __ 5 million (c) 800 thousand __ 8 million (d) 640 crore __ 60 billion
(3 marks)
4
EXERCISE 1.4 · 2 QUESTIONS
Nearest Neighbours and Populations of Cities
Q19
Write the five nearest neighbours (nearest thousand, ten thousand, lakh, ten lakh, crore) for: (a) 3,87,69,957 (b) 29,05,32,481
(3 marks)
Q20
The table gives the populations (2011 and 2001) of 20 Indian cities. Answer by approximation: (1) What is your general observation? (2) Give an appropriate title. (3) What 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) Which cities have almost doubled their population? (6) By what number should we multiply Patna's population to get a number close to Mumbai's?
(5 marks)
5
EXERCISE 1.5 · 9 QUESTIONS
Multiplication, Digits in Products and Estimates
Q21
Using the meaning of multiplication and division, explain why multiplying by 5 is the same as dividing by 2 and multiplying by 10.
(2 marks)
Q22
Find quick ways to calculate these products: (a) 2 × 1768 × 50 (b) 72 × 125 [Hint: 125 = 1000/8] (c) 125 × 40 × 8 × 25
(3 marks)
Q23
Calculate these products quickly. (a) 25 × 12 (b) 25 × 240 (c) 250 × 120 (d) 2500 × 12 (e) ____ × ____ = 120000000
(5 marks)
Q24
Multiply and find the pattern: 11 × 11, 111 × 111, 1111 × 1111; 66 × 61, 666 × 661, 6666 × 6661; 3 × 5, 33 × 35, 333 × 335; 101 × 101, 102 × 102, 103 × 103. Extend each pattern.
(5 marks)
Q25
Observe the number of digits in the two numbers being multiplied and their product in each case. Is there any connection? Roxie says that the product of two 2-digit numbers can only be a 3- or 4-digit number. Is she correct? Give the reasoning.
(3 marks)
Q26
Can multiplying a 3-digit number by another 3-digit number give a 4-digit number? Can multiplying a 4-digit number by a 2-digit number give a 5-digit number?
(3 marks)
Q27
Complete the pattern: 1-digit × 1-digit = 1-digit or 2-digit. 5-digit × 5-digit = __ or __ digits. 8-digit × 3-digit = __ or __ digits. 12-digit × 13-digit = __ or __ digits.
(3 marks)
Q28
Find out if you can reach the Sun in a lifetime if you travel 1000 km every day. (Distance from the Earth to the Sun ≈ 15 crore km.)
(2 marks)
Q29
Make reasonable assumptions and answer: (a) If a single sheet of paper weighs 5 grams, could you lift one lakh sheets together? (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, counting 1 coin every second?
(5 marks)
6
14 QUESTIONS
Exercise 1.6
Q30
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.
(3 marks)
Q31
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.
(3 marks)
Q32
Write a 9-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?
(3 marks)
Q33
Strike out 10 digits from the number 12345123451234512345 so that the remaining number is as large as possible.
(3 marks)
Q34
How far do you have to count to find two consecutive numbers which do not share an English letter in common? (The words 'zero' and 'one' share 'e' and 'o'; 'one' and 'two' share 'o'; 'two' and 'three' share 't'.)
(5 marks)
Q35
Suppose you write down all the numbers 1, 2, 3, 4, … The tenth digit you write is '1' and the eleventh digit is '0' (part of 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?
(5 marks)
Q36
A calculator has only '+10,000' and '+100' buttons. Write an expression describing the number of button clicks to be made for: (a) 20,800 (b) 92,100 (c) 1,20,500 (d) 65,30,000 (e) 70,25,700
(5 marks)
Q37
How many lakhs make a billion?
(2 marks)
Q38
You are given two sets of number cards numbered 1–9. Place a number card in each box (a 7-digit number and a 5-digit number) to get (a) the largest possible sum (b) the smallest possible difference of the two resulting numbers.
(3 marks)
Q39
Number cards: 4000, 13000, 300, 70000, 150000, 20, 5. Using any operations (each card once for a number) 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
(5 marks)
Q40
Find out how many coins should be stacked to match the height of the Statue of Unity (180 m). Assume each coin is 1 mm thick.
(2 marks)
Q41
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 an ocean approximately?
(2 marks)
Q42
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.
(2 marks)
Q43
Bald eagles fly as high as 4500–6000 m. Mount Everest is about 8850 m high. Aeroplanes fly as high as 10,000–12,800 m. How many times bigger are these heights compared to Somu's building (40 m)?
(3 marks)