Figure it Out - 1.1 (Page 50)
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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?
$1,00,000 - 75,000 = 25,000$
75,000 is 25,000 less than one lakh. -
2. The estimated population of Chintamani in the year 2024 is 1,06,000. How much more than one lakh is 1,06,000?
$1,06,000 - 1,00,000 = 6,000$
1,06,000 is 6,000 more than one lakh. -
3. By how much did the population of Chintamani increase from 2011 to 2024?
$1,06,000 - 75,000 = 31,000$
The population increased by 31,000.
Reading and Writing Numbers (Page 54)
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Write each of the numbers given below in words:
(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 thirty-eight -
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: 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: 10,00,235
1.2 Land of Tens (Pages 56-58)
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1. The Tedious Tens only has a $+10$ button. How many times should it be pressed to show:
(a) Five hundred? 50 times
(b) 780? 78 times
(c) 1000? 100 times
(d) 3700? 370 times
(e) 10,000? 1,000 times
(f) One lakh? 10,000 times
(g) 435 times 4,350 -
2. The Handy Hundreds only has a $+100$ button. How many times should it be pressed to show:
(a) Four hundred? 4 times
(b) 3,700? 37 times
(c) 10,000? 100 times
(d) Fifty three thousand? 530 times
(e) 90,000? 900 times
(f) 97,600? 976 times
(g) 1,00,000? 1,000 times
(h) 582 times 58,200
(i) How many hundreds are required to make ten thousand? 100 hundreds
(j) How many hundreds are required to make one lakh? 1,000 hundreds
(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.
Yes, any number that has a non-zero digit in the hundreds place (like 150) cannot be made by using only +10 or +1000 buttons alone, but can be made using the +100 button. -
3. 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? 10 times
(c) Fifty three thousand? 53 times
(d) 90,000? 90 times
(e) One Lakh? 100 times
(f) 153 times 1,53,000
(g) How many thousands are required to make one lakh? 100 thousands
Figure it Out - 1.2 (Page 58-60)
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5. Find a different way to get 5072 and write an expression for the same.
$(4 \times 1000) + (10 \times 100) + (7 \times 10) + (2 \times 1) = 5072$
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6. 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:
Way 1: $(8 \times 1000) + (3 \times 100) = 8300$
Way 2: $(7 \times 1000) + (13 \times 100) = 8300$
(b) 40629:
Way 1: $(4 \times 10000) + (6 \times 100) + (2 \times 10) + (9 \times 1) = 40629$
Way 2: $(3 \times 10000) + (10 \times 1000) + (5 \times 100) + (12 \times 10) + (9 \times 1) = 40629$
(c) 56354:
Way 1: $(5 \times 10000) + (6 \times 1000) + (3 \times 100) + (5 \times 10) + (4 \times 1) = 56354$
Way 2: $(4 \times 10000) + (16 \times 1000) + (2 \times 100) + (15 \times 10) + (4 \times 1) = 56354$
(d) 66666:
Way 1: $(6 \times 10000) + (6 \times 1000) + (6 \times 100) + (6 \times 10) + (6 \times 1) = 66666$
Way 2: $(5 \times 10000) + (16 \times 1000) + (5 \times 100) + (16 \times 10) + (6 \times 1) = 66666$
(e) 367813:
Way 1: $(3 \times 100000) + (6 \times 10000) + (7 \times 1000) + (8 \times 100) + (1 \times 10) + (3 \times 1) = 367813$
Way 2: $(2 \times 100000) + (16 \times 10000) + (6 \times 1000) + (18 \times 100) + (1 \times 10) + (3 \times 1) = 367813$ -
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?
Largest 3-digit number is 999 (using 27 clicks).
(b) 997 can be made using 25 clicks. Can you make 997 with a different number of clicks?
Yes, 997 can be made with $9+9+7 = 25$ clicks. Another way uses 34 clicks.
Figure it Out - 1.3 (Page 60)
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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) 5072: $(5 \times 1000) + (0 \times 100) + (7 \times 10) + (2 \times 1) = 5072$ (Total 14 clicks)
(b) 8300: $(8 \times 1000) + (3 \times 100) = 8300$ (Total 11 clicks)
(c) 40629: $(4 \times 10000) + (0 \times 1000) + (6 \times 100) + (2 \times 10) + (9 \times 1) = 40629$ (Total 21 clicks)
(d) 56354: $(5 \times 10000) + (6 \times 1000) + (3 \times 100) + (5 \times 10) + (4 \times 1) = 56354$ (Total 23 clicks)
(e) 66666: $(6 \times 10000) + (6 \times 1000) + (6 \times 100) + (6 \times 10) + (6 \times 1) = 66666$ (Total 30 clicks)
(f) 367813: $(3 \times 100000) + (6 \times 10000) + (7 \times 1000) + (8 \times 100) + (1 \times 10) + (3 \times 1) = 367813$ (Total 28 clicks) -
2. Do you see any connection between each number and the corresponding smallest number of button clicks?
Yes, the smallest number of button clicks is equal to the sum of the digits of the number in its standard decimal representation.
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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.
Because the calculator buttons correspond directly to the powers of 10 used in the Indian place value system ($1, 10, 100, 1000, 10000, 100000$), expressing a number with minimum clicks means writing it in its expanded form based on place values.
Figure it Out - 1.4 (Page 64)
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1. Read the following numbers in Indian place value notation and write their number names in both the Indian and American systems:
(a) 4050678:
Indian: Forty lakh fifty thousand six hundred seventy-eight
American: Four million fifty thousand six hundred seventy-eight
(b) 48121620:
Indian: Four crore eighty-one lakh twenty-one thousand six hundred twenty
American: Forty-eight million one hundred twenty-one thousand six hundred twenty
(c) 20022002:
Indian: Two crore two lakh twenty thousand two
American: Twenty million twenty-two thousand two
(d) 246813579:
Indian: Twenty-four crore sixty-eight lakh thirteen thousand five hundred seventy-nine
American: Two hundred forty-six million eight hundred thirteen thousand five hundred seventy-nine
(e) 345000543:
Indian: Thirty-four crore fifty lakh five hundred forty-three
American: Three hundred forty-five million five hundred forty-three
(f) 1020304050:
Indian: One arab two crore thirty lakh forty thousand fifty
American: One billion twenty million three hundred four thousand fifty -
2. Write the following numbers in Indian place value notation:
(a) One crore one lakh one thousand ten: 1,01,01,010
(b) One billion one million one thousand one: 1,01,01,001
(c) Ten crore twenty lakh thirty thousand forty: 10,20,30,040
(d) Nine billion eighty million seven hundred thousand six hundred: 90,80,70,600 -
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
Math Talk (Page 68)
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1. 4,63,128 + 4,19,682, Hasantika: "The sum is near 8,00,000 and is more than 8,00,000." Srestha: "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?
Both estimates are correct ranges/approximations, but Srestha's estimate (near 9,00,000) is closer to the actual sum.
(b) Will the sum be greater than 8,50,000 or less than 8,50,000? Why do you think so?
Greater than 8,50,000, because $4,63,128 + 4,19,682$ is greater than $4,50,000 + 4,00,000 = 8,50,000$.
(c) Will the sum be greater than 8,83,128 or less than 8,83,128? Why do you think so?
Less than 8,83,128, because $4,19,682$ is less than $4,20,000$ (and $4,63,128 + 4,20,000 = 8,83,128$).
(d) Exact value of $4,63,128 + 4,19,682 =$ 8,82,810 -
2. 14,63,128 - 4,90,020, Hasantika: "The difference is near 10,00,000 and is less than 10,00,000." Srestha: "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?
Both estimates give a sense, but Hasantika's estimate (near 10,00,000) is closer.
(b) Will the difference be greater than 9,50,000 or less than 9,50,000? Why do you think so?
Greater than 9,50,000, because subtracting 4,90,020 (which is less than 5,00,000) from 14,63,128 leaves more than $14,63,128 - 5,00,000 = 9,63,128$.
(c) Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think so?
Greater than 9,63,128, because we are subtracting 4,90,020, which is less than 5,00,000. Subtracting a smaller number results in a larger difference.
(d) Exact value of $14,63,128 - 4,90,020 =$ 9,73,108
Populations of Cities (Page 72)
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From the information given in the table, answer the following questions by approximation:
1. What is your general observation about this data? Share it with the class.
Most major Indian cities experienced significant population growth between 2001 and 2011.
2. How much is the population of Pune in 2011? Approximately, by how much has it increased compared to 2001?
Pune's population in 2011 was 31,15,431. It increased by approximately 6,00,000 compared to 2001 (25,38,473).
3. Which city's population increased the most between 2001 and 2011?
Bengaluru grew from 43,01,326 to 84,25,970, an increase of over 41 lakhs.
4. Are there cities whose population has almost doubled? Which are they?
Yes, Bengaluru, Hyderabad, Ahmedabad, Surat, and Vadodara have nearly doubled or more than doubled.
5. By what number should we multiply Patna's population to get a number/population close to that of Mumbai?
Patna's population needs to be multiplied by about 7 or 8 to reach Mumbai's population.
Figure it Out - 1.5 (Pages 80-82)
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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: 9876432105
(b) Smallest even number: 1023456798 -
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.
77,77,777 (Seventy-seven lakh seventy-seven thousand seven hundred seventy-seven)
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3. Write a 9-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?
Such a number is not possible. Thus, 0 such numbers exist.
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4. Strike out 10 digits from the number 12345123451234512345 so that the remaining number is as large as possible.
5555512345
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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: $(2 \times 10000) + (8 \times 100) = 20800$
(b) 92,100: $(9 \times 10000) + (21 \times 100) = 92100$
(c) 1,20,500: $(12 \times 10000) + (5 \times 100) = 120500$
(d) 65,30,000: $(653 \times 10000) + (0 \times 100) = 6530000$
(e) 70,25,700: $(702 \times 10000) + (57 \times 100) = 7025700$ -
8. How many lakhs make a billion?
10,000 lakhs
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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: $4000 \times (20 + 5) + 13000 = 1,13,000$
(b) 2,00,000: $150000 + 70000 - 13000 - 4000 - 300 = 1,99,700$
(c) 5,80,000: $150000 \times 4 - 20000$ (approximate calculation using cards)
(d) 12,45,000: Using available cards with multiplication/addition.
(e) 20,90,800: Using available cards with multiplication/addition. -
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?
At about 1000 km per day, a 12,000 km trip would take approximately 12 days.
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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.
Distance per day: $13,560 \div 11 \approx$ 1,233 km per day.
Distance per hour: $1,233 \div 24 \approx$ 51.4 km per hour. -
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 Ramu's building?
These heights are hundreds of times taller than Ramu's building.
