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Page 19: Take a sheet of paper, as large a sheet as you can find. Fold it once. Fold it again, and again. How many times can…
Page 20: Say you can fold a sheet of paper as many times as you wish. What would its thickness be after 30 folds? Make a…
Page 20: Now, what do you think the thickness would be after 30 folds? 45 folds? Make a guess.
Page 20: Fill the table below. After 26 folds, the thickness is approximately 670 m. Burj Khalifa in Dubai, the tallest…
Page 21: It might be hard to digest the fact that after just 46 folds, the thickness is more than 7,00,000 km. This is the…
Page 22: Which expression describes the thickness of a sheet of paper after it is folded 10 times? The initial thickness is…
Page 22: Express the number 32400 as a product of its prime factors and represent the prime factors in their exponential form.
Page 22: What is (–1)⁵? Is it positive or negative? What about (–1)56?
Page 22: What is 0², 0⁵? What about 0n?
Page 22: Is (–2)⁴ = 16? Verify.
Page 22: Express the following in exponential form:
Page 23: Express each of the following as a product of powers of their prime factors in exponential form.
Page 23: Write the numerical value of each of the following:
Page 23: How many rooms were there altogether?
Page 23: How many diamonds were there in total? Can we find out by just one multiplication using the products above?
Page 24: 3⁷ can also be written as 3²×3⁵. Can you reason out why?
Page 24: This can be easily extended to products where exponents are the same letter-numbers. Write the product p⁴×p⁶ in…
Page 24: Use this observation to compute the following.
Page 24: Is 210 also equal to (2⁵)²? Write it as a product.
Page 24: Write the following expressions as a power of a power in at least two different ways:
Page 25: In the middle of a beautiful, magical pond lies a bright pink lotus. The number of lotuses doubles every day in this…
Page 25: Write the number of lotuses (in exponential form) when the pond was —
Page 25: There is another pond in which the number of lotuses triples every day. When both ponds had no flowers, Damayanti…
Page 25: What if Damayanti had changed the order in which she placed the flowers in the lakes? How many lotuses would there be?
Page 25: Can this product be expressed as an exponent mn, where m and n are some counting numbers? Use this observation to…
Page 25: Simplify 10⁴/5⁴ and write it in exponential form.
Page 26: Estu has 4 dresses and 3 caps. How many different ways can Estu combine the dresses and caps?
Page 26: Roxie has 7 dresses, 2 hats, and 3 pairs of shoes. How many different ways can Roxie dress up?
Page 26: Estu and Roxie came across a safe containing old stamps and coins that their great-grandfather had collected. It was…
Page 27: How many 5-digit passwords are possible?
Page 27: How many passwords are possible with such a lock?
Page 27: Think about how many combinations are possible in different contexts. Some examples are — (i) Pincodes of places in…
Page 27: Imagine a line of length 16 units. Erasing half of it would result in — Erasing half one more time would result in —…
Page 27: What is 2100÷225 in powers of 2?
Page 28: Why can’t n be 0?
Page 28: We have not covered the case when the exponent is 0; for example, what is 2⁰?
Page 28: When a line of length 2⁴ units is halved 5 times, When a line of length 2⁴ units is halved 10 times, we get…
Page 29: We had required a and b to be counting numbers. Can a and b be any integers? Will the generalised forms still hold true?
Page 29: Write equivalent forms of the following.
Page 29: Simplify and write the answers in exponential form.
Page 29: Let us arrange the powers of 4 along a line.
Page 30: Can we say that 16384 (4⁷) is 16 (4²) times larger than 1024 (4⁵)?
Page 30: How many times larger than 4–2 is 4²?
Page 30: Use the power line for 7 to answer the following questions.
Page 30: Write these numbers in the same way: (i) 172, (ii) 5642, (iii) 6374.
Page 30: How can we write 561.903?
Page 31: (i) The Sun is located 30,00,00,00,00,00,00,00,00,000 m from the centre of our Milky Way galaxy. (ii) The number of…
Page 32: The distance between the Sun and Saturn is 14,33,50,00,00,000 m =1.4335×1012 m. The distance between Saturn and…
Page 32: The number line below shows the distance between the Sun and Saturn (1.4335×1012 m). On the number line below, mark…
Page 32: Express the following numbers in standard form.
Page 33: Nanjundappa wants to donate jaggery equal to Roxie’s weight and wheat equal to Estu’s weight. He is wondering how…
Page 33: Roxie wonders, "Instead of jaggery if we use 1-rupee coins, how many coins are needed to equal my weight?". How can…
Page 34: Estu asks, "What if we use 5-rupee coins or 10-rupee notes instead? How much money could it be?" Make an instinctive…
Page 34: Estu says, "When I become an adult, I would like to donate notebooks worth my weight every year". Roxie says, "When…
Page 34: Roxie and Estu overheard someone saying — "We did pādayātra for about 400 km to reach this place! We arrived early…
Page 35: How many times can a person circumnavigate (go around the world) the Earth in their lifetime if they walk non-stop?…
Page 35: Roxie tells Estu about a science-fiction novel she is reading where they build a ladder to reach the moon, "… I…
Page 36: We have to find out how many 20 cm make 3,84,400 km.
Page 36: 0 cm+20 cm→20 cm+20 cm→40 cm+20 cm→60 cm+20 cm→… (1,92,20,00,000 steps)Some examples of exponential growth we have…
Page 36: Last year, we learnt about lakhs and crores, as well as millions and billions. A lakh is 10⁵ (1,00,000), a crore is…
Page 38: With a global human population of about 8×10⁹ and about 4×10⁵ African elephants, can we say that there are nearly…
Page 38: Calculate and write the answer using scientific notation: (i) How many ants are there for every human in the world?…
Page 38: A different way to say your age — days and hours old.
Page 39: If you have lived for a million seconds, how old would you be?
Page 39: We shall look at approximate times and timelines of some events and phenomena, and use powers of 10 to represent and…
Page 39: 10⁵ seconds ≈ 1.16 days and 10⁶ seconds ≈ 11.57 days. Think of some events or phenomena whose time is of the order…
Page 42: Calculate and write the answer using scientific notation: (i) If one star is counted every second, how long would it…
Page 42: In the Lalitavistara, a Buddhist treatise from the first century BCE, we see number-names for odd powers of ten up…
Page 43: Observe the names million (10⁶), billion (10⁹), trillion (1012), quadrillion (1015), quintillion (1018), sextillion…
Page 44: Find out the units digit in the value of 2224÷432? [Hint: 4=2²]
Page 44: There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would there be after…
Page 44: Write the given number as the product of two or more powers in three different ways. The powers can be any integers.
Page 44: Examine each statement below and find out if it is ‘Always True’, ‘Only Sometimes True’, or ‘Never True’. Explain…
Page 44: Simplify and write these in the exponential form.
Page 44: If 12²=144, what is —
Page 45: Circle the numbers that are the same —
Page 45: Identify the greater number in each of the following —
Page 45: A dairy plans to produce 8.5 billion packets of milk in a year. They want a unique ID (identifier) code for each…
Page 45: 64 is a square number (8²) and a cube number (4³). Are there other numbers that are both squares and cubes? Is there…
Page 45: A digital locker has an alphanumeric (it can have both digits and letters) passcode of length 5. Some example codes…
Page 45: The worldwide population of sheep (2024) is about 10⁹, and that of goats is also about the same. What is the total…
Page 45: Calculate and write the answer in scientific notation: (i) If each person in the world had 30 pieces of clothing,…
Page 45: What was the date 1 arab/1 billion seconds ago?
Page 47: Find a partner to play this game with. In 10 seconds, the person who writes a number or an expression, using only…

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