Question 1

What would the thickness of a sheet of paper be after 30 folds? Assume that the thickness of the sheet is 0.001 cm. (Page 19)

Accepted Answer

Here, 2
30
= 1,073,741,824
Final thickness = 0.001 × 1,073,741,824
= 1,073,741.824 cm
= 10,737.41824 meters (1 m = 100 cm)
= 10.74 kilometers (1 km = 1000 m)
Hence, after 30 folds, the thickness of the paper would be approximately 10.74 kilometers.

Question 2

Fill in the table below. (Use the thickness of the sheet 0.001 cm) (Page 20)

Accepted Answer

The height of folded paper will blow our minds. Here are some equivalent heights based on the number of folds.
After 10 folds, the thickness is just above 1 cm (1.024 cm).
After 17 folds, the thickness is about 131 cm (a little more than 4 feet).
At 24 folds, the paper is nearly as tall as the Statue of Unity.
At 25 times its height, it becomes taller than the Statue of Unity and the Eiffel Tower.
At 26 folds, the paper becomes taller than the Statue of Unity and the Eiffel Tower, but it is still slightly shorter than Burj Khalifa.
At 27 folds, the paper becomes 1.34 km thick, which is taller than the Burj Khalifa, the world’s tallest building.
At 33 folds, the thickness reaches 85.9 km, bringing it close to the Karman Line, the official edge of outer space!
By 36 folds, the paper’s thickness is around 687 km, making it taller than the orbit of the International Space Station (ISS)!
After 45 folds, the paper becomes about 351,844 km thick, which is almost the distance from Earth to the Moon!
It may seem unbelievable, but after just 46 folds, the thickness of a paper exceeds 700,000 kilometers.
That’s the incredible power of exponential (multiplicative) growth, small beginnings that grow unimaginably big, very fast!

Question 3

What do you think the thickness would be after 30 folds? 36 folds? Try to match it to a real-world height.

Accepted Answer

After 30 folds, the paper’s thickness exceeds 10.74 km, which is higher than Mount Everest and even higher than most airplanes fly.
After 36 folds, the paper becomes about 687 km thick, which is almost the distance from Earth to the exosphere (Earth’s outermost atmospheric layer).
2.2 Exponential Notation and Operations
Intext Questions

Question 4

What is 0
2
, 0
5
?

Accepted Answer

0
2
= 0 × 0 = 0
0
5
= 0 × 0 × 0 × 0 × 0 = 0

Source: This question is from Power Play, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Power Play: Power Play, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Power PlayQ1: What would the thickness of a sheet of paper be after 30 folds? Assume that the thickness of the...
Q10: 64 is a square number (8 2 ) and a cube number (4 3 ). Are there other numbers that are both...
Q11: A digital locker has an alphanumeric (it can have both digits and letters) pass code of length 5....
Q13: Calculate and write the answer in scientific notation: (i) If each person in the world had 30...
Q14: What was the date 1 arab/1 billion seconds ago?
Practice more questions from Power Play &mdash; Mathematics, Class 8 CBSE

Question 5

What is 0
n
?

Accepted Answer

0
n
= 0 × 0 × 0 × …… n times = 0
Figure It Out (Pages 22-23)

Source: This question is from Power Play, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Power Play: Power Play, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Power PlayQ1: What would the thickness of a sheet of paper be after 30 folds? Assume that the thickness of the...
Q10: 64 is a square number (8 2 ) and a cube number (4 3 ). Are there other numbers that are both...
Q11: A digital locker has an alphanumeric (it can have both digits and letters) pass code of length 5....
Q13: Calculate and write the answer in scientific notation: (i) If each person in the world had 30...
Q14: What was the date 1 arab/1 billion seconds ago?
Practice more questions from Power Play &mdash; Mathematics, Class 8 CBSE

Question 6

Estu says, “When I become an adult, I would like to donate notebooks worth my weight every year.”
Roxie says, “When I grow up, I would like to do annadana (offering grains or meals) worth my weight every year.”
How many people might benefit from each of these offerings in a year? Again, guess first before finding out. (Page 34)

Accepted Answer

Quick Guess
Estu’s notebook donation may benefit 100 to 200 students could benefit each year.
Roxie’s meal offering is perhaps enough grains or meals to feed 150 to 300 people annually.
Estimate and calculate
Assumptions:
Estu’s weight ~ 38 kg
Cost of 1 notebook ~ ₹ 20
Roxie’s weight is ~ 45 kg
Cost of 1 kg of grain or meal donations ~ ₹ 30
Meal cost per person per day ~ ₹ 15
Estu’s donation: Notebooks worth her weight
Value of donation = 38 × ₹ 20 = ₹ 760
If each student needs 2 notebooks:
No. of students helped = ₹ 760 ÷ ₹ 40 = 19
19 students could receive notebooks each year.
Roxie’s donation: Grains or Meals worth her weight
Value of donation = 45 × ₹ 30 = ₹ 1350
Each meal costs = ₹ 15
∴ No. of people to whom meal can be provided = ₹ 1350 ÷ 15 = 90
90 people could receive a single meal, or fewer people could eat multiple meals per year.

Question 7

Roxie and Estu overheard someone saying, “We did a padayatra for about 400 km to reach this place! We arrived early this morning.” How long ago would they have started their journey? Find answers by making necessary assumptions and approximations. Do guess first before calculating to check how close your guess was! (Page 34)

Accepted Answer

Guessing
If someone walked 400 km on foot, how long might it take?
Let us guess they walked about 25-30 km per day.
∴ Rough guess for number of days = 400 ÷ 25 = 16 days
Or maybe 13-20 days, depending on speed and rest.
Estimating and Calculating
Let daily distance walked = 30 km
Distance covered = 400 km
Number of days = 400 ÷ 30
= 13.3 days
~ 13 to 14 days

Question 8

How many times can a person circumnavigate (go around the world) the Earth in their lifetime, if they walk non-stop? Consider the distance around the Earth as 40,000 km. (Page 35)

Accepted Answer

Assumptions
Circumference of Earth = 40,000 km
Average walking speed = 5 km/hr
Maximum walking hours per day = 8 hours (approx.) years spent walking.
Let’s assume an active span of 60 years (ages 15 to 75)
Distance covered in 1 day = 8 × 5 = 40 km
Total days walked over = 60 × 365 = 21,900 days
Total lifetime distance walked = 21900 × 40 = 876000 km
Earth circumnavigations = 876000 + 40,000 = 21.9 times
Linear Growth Vs Exponential Growth

Question 9

A dairy plans to produce 8.5 billion packets of milk in a year. They want a unique ID (identifier) code for each packet. If they choose to use the digits 0-9, how many digits should the code consist of?

Accepted Answer

Total no. of packets produced in a year = 8.5 billion
∴ Number of codes required = 8.5 × 10
9
codes
For ID digits to be taken from 0 to 9.
So each digit has 10 choices.
To make code with n digits, the total number of possible codes = 10
n
∴ 10
n
≥ 8.5 × 10
9
10
9
= 1,00,00,00,000
The smallest value of n that satisfies
10
n
≥ 8.5 × 10
9
is 10.
Hence number of digits the code should consist of 10
10
.

Question 10

64 is a square number (8
2
) and a cube number (4
3
). Are there other numbers that are both squares and cubes? Is there a way to describe such numbers in general?

Accepted Answer

Yes, other numbers are both squares and cubes.
General Rule: A number is both a perfect square and a perfect cube if and only if it is a perfect sixth power, i.e., it can be written as x
6
for some integer x.

Question 11

A digital locker has an alphanumeric (it can have both digits and letters) pass code of length 5. Some example codes are G89P0, 38098, BRJKW, and 003AZ. How many such codes are possible?

Accepted Answer

Number of letters (A-Z) = 26
Number of digits (0-9) = 10
So, each character in the passcode can be any of the 36 alphanumeric characters.
Also, each of the 5 positions has 36 options.
Total codes = 36
5
= 6,04,66,176
Hence number of possible 5-character alphanumeric passcodes is 6,04,66,176.

Question 12

The worldwide population of sheep (2024) is about 10
9
, and that of goats is also about the same. What is the total population of sheep and goats?
(i) 20
9
(ii) 10
11
(iii) 10
10
(iv) 10
18
(v) 2 × 10
9
(vi) 10
9
+ 10
9

Accepted Answer

Sheep population = 10
9
Goat population = 10
9
Total population of sheep and goats = 10
9
+ 10
9
= 2 × 10
9

Source: This question is from Power Play, Mathematics &mdash; Class 8, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Power Play: Worldwide, Population, Sheep, Goats, Same, Total. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 8 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Power PlayQ1: What would the thickness of a sheet of paper be after 30 folds? Assume that the thickness of the...
Q10: 64 is a square number (8 2 ) and a cube number (4 3 ). Are there other numbers that are both...
Q11: A digital locker has an alphanumeric (it can have both digits and letters) pass code of length 5....
Q13: Calculate and write the answer in scientific notation: (i) If each person in the world had 30...
Q14: What was the date 1 arab/1 billion seconds ago?
Practice more questions from Power Play &mdash; Mathematics, Class 8 CBSE

Question 13

Calculate and write the answer in scientific notation:
(i) If each person in the world had 30 pieces of clothing, find the total number of pieces of clothing.
(ii) There are about 100 million bee colonies in the world. Find the number of honeybees if each colony has about 50,000 bees.
(iii) The human body has about 38 trillion bacterial cells. Find the bacterial population residing in all humans in the world.
(iv) Total time spent eating in a lifetime in seconds.

Accepted Answer

(i) World population = 8.2 billion = 8.2 × 10
9
Pieces of clothing = 30 pieces per person
Total pieces of clothing = 8.2 × 10
9
× 30
= 246 × 10
9
= 2.46 × 10
11
pieces of clothing
(ii) No. of bee colonies = 100 million = 1 × 10
8
No. of bee per colony = 50,000 = 5 × 10
4
Total no. of bees = 1 × 10
8
× 5 × 10
4
= 5 × 10
8+4
= 5 × 10
12
honeybees
(iii) No. of bacterial cells per human body = 38 trillion = 3.8 × 10
13
World population (approx.) = 8.2 billion = 8.2 × 10
9
Total bacterial population = 3.8 × 10
13
× 8.2 × 10
9
= 31.16 × 10
13+9
= 31.16 × 10
22
(iv) Let average eating time per day = 1.5 hours
In seconds = 1.5 × 60 × 60 = 5400 = 5.4 × 10
3
and an average person’s lifetime (approx.) = 70 years
In seconds = 70 × 365 × 24 × 60 × 60
= 161,148,960,000
= 1.61 × 10
11
Total time spent in eating = 5.4 × 10
3
× 1.61 × 10
11
= 8.694 × 10
3+11
= 8.7 × 10
14
seconds

Question 14

What was the date 1 arab/1 billion seconds ago?

Accepted Answer

1 arab / 1 billion = 10
9
minutes = $\frac {1,000,000,000}{60}$
hours = $\frac{1,000,000,000}{60 \times 60}$
days = $\frac{1,000,000,000}{60 \times 60 \times 24}$
years = $\frac{1,000,000,000}{365 \times 60 \times 60 \times 24}$
Now, we go back to the calendar.
So, it is approx. 31 years, 8 months, and 15 days.
Let today’s date = 1 Jan, 2026
After 31 years and 8 months and 15 days before the date was 24th April, 1994 (approx.)