Complete the Ganita Prakash Class 8 Worksheet and NCERT Class 8 Maths Chapter 2 Power Play Worksheet with Answers before your unit tests for better preparation.
Power Play Worksheet Class 8
Class 8 Maths Power Play Worksheet
Power Play Class 8 Ganita Prakash Worksheet
An impossible ventureat
At the school fair, Aman and Ariamtka stopped at a brLqht, colourful stall. The shopkeeper was rolling up a gtant scroll of cloth.
Aman: “Uncle, why are you rolling it? Wouldn’t folding be easter?”
Shopkeeper: “Rolling keeps it neat and easy to store. Folding such a big cloth would be quite difficult, don’t you think?”
Anamika: “Oh no, folding is neater! My morn keeps all our clothes folded in the cupboard. Why can’t we fold thts, too?”
The shopkeeper’s eyes twinkled. “Alright then, Let’s try your way! But here is a twist every time you fold it, its thickness doubles. Keep an eye on how thick it becomes, and tell me what you discover.”
Question 1.
The cloth was initially 0.2 mm thick. Aman started folding and observed the thickness after each fold.
. After the first fold, the thickness became 0.4 mm
. After the second fold, the thickness became 0.8 mm
. After the thlrd fold, the thickness became 1.6 mm
(a) Complete the table to find the missing thicknesses.
| Fold | Thickness (mm) |
| Align ‘O’ (unfolded) | 0.2 mm |
| 1 | 0.4 mm |
| 2 | 0.8 mm |
| 3 | 1.6 mm |
| 5 | |
| 8 | |
| 10 | |
| 12 | |
| 15 | |
| 20 |
Answer:
6.4 mm; 51.2 mm; 204.8; 819.2 mm; 6553.6 mm; 209, 715.2 mm
(b) After 15 folds, compare the cloth’s thickness with the height of a bus (≈ 3 m). Which is greater?
Answer:
(b) Cloth’s thickness is greater than the height of bus.
(c) After 20 folds, does the thickness cross 200 m (the height of a tall tower)?
Answer:
Yes
(d) If Aman continued folding the cloth and somehow managed to make 25 folds, the thickness would be:
(i) less than 100 m.
(ii) between 100 m and 200 m.
(iii) more than 200 m.
(iv) more than 500 m.
Answer:
more than 500 m
(e) The initial thickness of the cloth is 0.2 mm.
Write a general expression for the thickness of the cloth after n folds.
Answer:
0.2 × 2 mm
Question 2.
Is it correct to say that folding a 0.1 mm-thick paper five times will result in a thickness of 5 × 0.1 mm?
Answer:
No.
Exponential Notation and Operations
Question 3.
During the holidays, Ravi visited his aunt’s stationery shop. Aunt said, “In this shop, each bag has 3 boxes. Each box contains 3 packets. Each packet has 3 markers. Can you work out the total number of markers in one packet?”
Help Ravi to answer the questions given below:
(a) Write the total number of markers in one bag as repeated multiplication and in exponential form.
(b) How many markers will there be if there are 4 such bags? Express the number of markers in exponential form.
Answer:
(a) 3 × 33 markers
(b) 108 markers or 4 × 33 or 22 × 33 markers
Question 4.
Express the following in. exponential form:
(a) 8 × 8 × 8 × 8× 8
(b) z × z × z
(c) p × p × p × p × p × p
(d) 6 × 6 × 9 × 9 × 9
(e) 2 × 2 × 2 × m × m
(d) a × a × b × b × b × c × c × c × c
Answer:
(a) 85
(b) z3
(c) p6
(d) 62 × 93
(e) 23 × m2
(f) a2 × b3 × c2
Question 5.
Express each of the following as a product of powers of their prime factors in exponential form:
(a) 432
(b) 784
(d) 1500
Answer:
(a) 24 × 33
(b) 24 × 72
(c) 22 × 72 × 5
(d) 22 × 53 × 3
Question 6.
Is it true that exponential growth means a quantity increases by the same amount each time?
Answer:
No.
Question 7.
What is (-1)9? Is it positive or negative? What about (-1)24?
Answer:
-1, negative 1
Question 8.
Find the numerical value of each of the following:
(a) 52 × 23
(b) 4 × 73
(c) (—2)3 × (9)3
Answer:
(a) 200
(b) 1372
(c) 5832
Question 9.
Write the following expressions as a power of a power in at least two different wags:
(a) 109
(b) 218
(c) 915
(d) 1121
Answer:
(a) (101)9 or (103)3
(b) (212)4 or (214)2
(c) (93)5 or (95)3
(d) (113)7 + (117)3
Counting fireflies
Question 10.
In a forest, a single glowing firefly appeared. Each night, the number of fireflies doubled. After 20 nights, the whole forest sparkled with fireflies.
(a) On which night was the forest half full?
Answer:
19th
(b) Write the number of fireflies in exponential form when the forest is:
(i) Fully covered
(ii) Half covered
(iii) One-third covered
Answer:
(i) 219
(ii) 218
(iii) \(\frac{1}{3} \times 2^{19}\)
(c) A scientist counts 128 fireflies on one night. Which night could it be?
Answer:
8th
(d) If after 4th night, number of fireflies’ quadruples, then what is the number of fireflies on 7th night in exponential form?
Answer:
29
Question 11.
Simplify the following using laws of exponents:
(a) 72 × 72 = ______
(b) a2 × a2 =
(c) (32)3 =
(d) (x3)2 =
(e) (p2q3)2 =
(f) m6 + m2 =
(g) (105)2 + 102 =
(h) (53)2 ÷ 54 =
(i) (m5 × m3) ÷ (m2 × m4) =
Answer:
(a) 16807
(b) a6
(c) 36
(d) x6
(e) p4q6
(f) m4
(g) 1000
(h) 25
(i) m2
Question 12.
A bacteria culture triples every hour. Write the number of bacteria after 6 hours if it starts with 1.
Answer:
729
Question 13.
A square has side 32 cm. Write its area in exponential form.
Answer:
(32)2 cm2
Question 14.
A company’s machines produce 52 items per hour. How many items will it produce in 8 hours? Write in exponential form.
Answer:
23 × 52 items
Question 15.
A tree doubles its height every year. If it is h metres tall now, write its height after 4 years using exponents. Also give a general formula for it.
Answer:
h × 24, h × 2n
How Many Combinations
Question 16.
Ritu saw a digital safe with 8 slots. Each slot could use digits 0-9.
“How many possible codes are there for this safe?” she wondered.
Each slot has 10 choices.
So, total codes = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 108
= 10,00,00,000 codes (10 crore codes).
Now, Ritu thought, “What if instead of digits, each slot could have one of the 26 English letters?” How many codes would be possible then?
Answer:
(26)8 codes
Question 17.
In some states, vehicle registration numbers are written as:
2 English Alphabets + 4 digits
For example, DL 4521, MH 0934. How many such registration numbers are possible?
Answer:
262 × 104 or 67,60,000
The Other side of Powers
Question 18.
Aarav was helping his father at the pharmacy when he noticed a medicine bottle labeled Dosage: 2.5 × 10-3 litres
Aarav was confused. He asked, “Papa, what does 10-3 mean here? How can a power be negative?”
His father smiled and explained:
• 10-3 = \(\frac{1}{10^3}=\frac{1}{1000}\)
• So, 2.5 × 10-3 litres = \(\frac{2.5}{1000}\) litres = 0.0025 litres
“That’s why the quantity of medicine is given in millilitres (mL) because 0.0025 litre = 2.5 mL,” said Father.
Aarav then understood that negative powers are used to represent very small quantities, especially in science and medicine.
(a) Aarav saw another medicine label, which says 1.2 × 10-4 litres. Convert this quantity into millilitres.
Answer:
0.12 mL
(b) If a patient needs 5 mL of the same medicine, express this quantity in litres using powers of 10.
Answer:
5 × 10-3 litres.
(c) Aarav’s father explained that 10-3 means 1 divided by 1000. Following the same idea, what does 10-6 represent?
Answer:
1 divide by 1000000
(d) A second medicine requires a dosage of 7 × 10-4 litres. How many millilitres is this?
Question 19.
Write the equivalent forms for the following:
(a) 4-4
(b) (-9)-3
(c) 20-5
Answer:
(a) \(\frac{1}{(4)^4}\)
(b) \( \frac{1}{(-9)^3}\)
(c) \( \frac{1}{(20)^{50}}\)
Question 20.
Simplify and write the answers in exponential form.
(a) 2-5 × 28
(b) 42 × 4-6 × 44
(c) 84 × (-4)-4
(d) 7p × 7q × 7pq
Answer:
(a) (2)3
(b) (4)0
(c) (2)4
(d) (7)p+q+pq
Question 21.
Which is larger: 5-2 or 2-3?
Answer:
2-3
Question 22.
Check the given numbers as the product of two or more powers in three different wags. The powers can be any integers.
(a) 164
(b) 2435
(c) 81-3
Answer:
(a) (162) × (162),(28 × 28), (44 × 44)
The answers may vary
Question 23.
If 152 = 225, then find the following:
(a) 1.52 =
(b) 0.152 =
(c) 0.0152 =
Answer:
(a) 2.25
(b) 0.0225
(c) 0. 000225
When Zero is in Power!
Question 24.
Ria and Kabir were playing a number game after school. Kabir wrote on tke board: “103 ÷ 103 = ?”
Ria smiled and said, “That’s easy! When we divide numbers with the same base, we subtract the exponents. So, 103-3 = 10°
Kabir looked surprised. “But what does 10° mean?”
Ria replied confidently, “Anything raised to the power of zero is 1. So, the answer is 1!”
Kabir dapped his bands. “Wow, the zero power rule is amazing!”
(a) Kabir is learning about the zero exponent rule. What is the value of 15°?
(b) Ria solved the problem 1000 -5- 1000. Express this expression using exponents and show that the result is equal to 1.
Answer:
(a) 1
(b) 103 ÷ 103 = 1
Question 25.
If a baker prepares 50° cakes, how many cakes are prepared by him actually?
Answer:
1 cake
Power Lines
Question 26.
Use the power line for 5 to answer the following questions in exponential form:
| Powers of 5 | Value |
| 57 | 78125 |
| 56 | 15625 |
| 55 | 3125 |
| 54 | 625 |
| 53 | 125 |
| 52 | 25 |
| 51 | 5 |
| 50 | 1 |
| 5-1 | \(\frac{1}{2}\) |
| 5-2 | \(\frac{1}{25}\) |
Questions
(a) 125 × 125 =
(b) 15625 ÷ 25 =
(c) 253
(d) 3125 ÷ 125 =
(e) 15625 × \(\frac{1}{125}\) =
(f) \(\frac{1}{125}\) × \(\frac{1}{125}\) =
(g) 652 × 625 =
(h) 3125 ÷ 78125 =
(i) 15625 × \(\frac{1}{125}\) =
(j) 125 ÷ 3125 =
Answer:
(a) 57
(b) 54
(c) 56
(d) 52
(e) 53
(f) 5-6
(g) 56
(h) 5-2
(i) 53
(j) 5-2
Powers of 10
Question 27.
Write the following numbers in powers of 10:
(a) 172
(b) 5642
(c) 6374
Answer:
(a) 1 × 102 + 7 × 101 + 2 × 100
(b) 5 × 103 + 6 × 102 + 4 × 100
(c) 6 × 103 + 7 × 101 + 4 × 100
Question 28.
Express the Jollowiag decimals in. powers of 10:
(a) 45.3
(b) 0.607
(c) 19.045
Answer:
(a) 4 × 101 + 5 × 100 + 3 × 10-1
(b) 6 × 10-1 + 7 × 10-3
(c) 1 × 101 + 9 × 100 + 4 × 10-2 + 5 × 10-3
Question 29.
The population of a town is 3,45,210. Write it using powers of 10.
Answer:
3 × 105 + 4 × 104 + 5 × 103 + 4 × 100 + 1 × 101
Question 30.
A machine measures the distance covered by a car as 128.76 km. Express this using powers of 10.
Answer:
1 × 102 + 2x 101 + 8x 100 + 7 × 10-3
Question 31.
A medicine bottle shows 0.025 L. Write this in expanded form with powers of 10.
Answer:
2 × 10-2 + 5 × 10-3L
Scientific Notation
Question 32.
Express the following in standard form.
(a) The speed of light = 300,000,000 m/s.
(b) The mass of a dust particle = 0.000000000753 kg.
(c) The radius of a hydrogen atom = 0.00000005 cm.
Answer:
(a) 3 × 108 m/s
(b) 7.35 × 10-10 kg
(c) 5 × 10-8 cm
Question 33.
Express the following numbers in standard form.
(a) 48,750 =
(b) 92,305 =
(c) 5,60,00,000 =
(d) 38,50,00,00,000 =
Answer:
(a) 4. 875 × 104
(b) 9. 2305 × 104
(c) 5.6 × 107
(d) 3.85 × 1010
Question 34.
The number line below shows the distance between the Sun and Jupiter (7.78 × 1011 m). On the number line below, mark the relative position of Mars. The distance between the Sun and Mars is 2.28 × 1011 m.
Linear Growth vs Exponential Growth
Question 35.
If a car moves 12 km every hour, how far will it travel in 15 hours? Is it a linear or exponential growth?
Answer:
180. km, Linear growth
Question 36.
If the population of bacteria doubles every 4 hours, starting with 50, how many will there be after 20 hours? Is it a linear or exponential growth?
Answer:
1600 becteria, Exponential growth
Question 37.
A ladder with steps 25 cm apart is imagined from Earth to the Sun (distance = 15 crore km). How many steps would be needed for such a ladder?
Answer:
6 × 1011 steps
Getting a Sense for Large Numbers
Question 38.
Kartik’s father gives him pocket money every day. On the first day, he gets only ?1. But from the second day onward, his pocket money doubles each day. How much pocket money will Kartik receive on the 30th day? What will be the total pocket money kartik collects over all 30 days?
Answer:
₹ 536,870,912; ₹1,073,741,823
Question 39.
The estimated total number of bacteria on Earth is about 5 × 1030 The current world human population is about 8 × 109.
(a) Estimate how many bacteria are there for every human on Earth.
(b) Express your answer in standard form.
Answer:
(a) 0.625 × 1021
(b) 6. 25 × 1020
Question 40.
The average thickness of a standard aluminium foil is about 1 × 10-5 m. The average distance from the Earth to the Moon Is about 3.84 × 108 m.
(a) If you stacked aluminium foils one on top of another, how many sheets would you need to reach the Moon? (Give your answer in scientific notation).
Answer:
3.84 × 1013 sheets
(b) If someone says they have lived for 10q seconds, how many years old are they approximately? (Use 1 year ≈ 3.15 × 107 seconds.)
Answer:
32 years (App)
Question 41.
If one galaxy is counted every second, how long (in seconds) would it take to count all the galaxies in the observable universe? Use the estimate that there are about 2 × 1012 galaxies.
Answer:
2 × 1012 Seconds
Question 42.
If one grain of sand is counted every second, how long would it take to count all the grains (around 7500000000000000000) of sand on Earth? Answer in seconds using scientific notation.
Answer:
7.5 × 1018s
Worksheet On Power Play Class 8
A. Choose the correct option.
1. Which of the following equals 210?
(a) 100
(b) 512
(c) 1024
(d) 2048
Answer:
(c) 1024
2. Which of the following is the correct exponential form of 648?
(a) 23 × 34
(b) 24
(c) 22 × 33
(d) 23 × 33
Answer:
(a) 23 × 34
3. If the population of a town doubles every 5 years, then after 20 years it will become:
(a) 2 times
(b) 4 times
(c) 8 times
(d) 16 times
Answer:
4. Which of these is equal to 10-33?
(a) 1000
(b) 0.001
(c) \(\frac{1}{10000}\)
(d) 100
Answer:
(b) 0.001
5. Which one is written correctly in scientific notation?
(a) 25 × 105
(b) 2.5 × 105
(c) 0.25 × 105
(d) 25.0 × 104
Answer:
(b) 2.5 × 105
Directions. (For Q.6 – 7): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A). .
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
6. Assertion (A): 2(-4) = \(\frac{1}{16}\).
Reason (R): Negative powers represent reciprocals of positive powers.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
7. Assertion (A): Scientific notation makes reading very large or very small numbers easy.
Reason (R): It expresses numbers as a product of a number between 1 and 10 and a power of 10.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B. Fill in the blanks.
1. am × an = a(m+___)
Answer:
n
2. The standard form of 59,000 is _______
Answer:
5.9 × 104
3. The value of (-2)4 is _______.
Answer:
16
4. The exponential form of 32400 is _______.
Answer:
3.24 × 104
5. n° = _______, where n ≠ 0.
Answer:
1
C. State whether the following statements are true (T) or false (F).
1. n(-a) = \(\frac{1}{n^a}\), for n ≠ 0.
Answer:
True
2. In linear growth, growth increases by the same amount each time, while in exponential growth, growth increases by some factor every time.
Answer:
True
3. The number of vehicle registration numbers with 2 letters and 4 digits is 226 × 104.
Answer:
True
4. Linear growth is faster than exponential growth.
Answer:
False
5. Every large number can be expressed in scientific notation.
Answer:
True
D. Solve the following.
Question 1.
A piece of paper of thickness 0.001 cm is folded 16 times. Now, find its thickness.
Answer:
65. 536 cm
Question 2.
A pond gets fully covered with lotuses in 16 days. On which day is it half full?
Answer:
15th
Question 3.
Express O.0005q in standard form.
Answer:
5.9 × 10-4
Question 4.
A dairy produces 8.5 biLlion packets of milk a year. Find the minimum number of digits required
f or a unique code for each packet.
Answer:
10 digits
Question 5.
Compare the values: 43 and 34
Answer:
34 > 43
Question 6.
If you stack sheets of paper to reach the Moon (distance 3,84,400 km), how many sheets would be needed if each sheet is 0.001 cm thick?
Answer:
3.84 × 1013 sheets
Question 7.
If you count 1 star per second, estimate how many years it will take to count all the stars. The estimated number of stars in the universe is 2 × 1023.
Answer:
2 × 1023 seconds
Question 8.
Why is 64 called a perfect sixth power?
Answer:
Do it yourself
Case-Based Questions
Question 9.
The mass of the Earth is 5,976,000,000,000,000,000,000,000 kg and its radius is 6.37 × 106 m. Moon is the natural satellite of Earth. The mass of the Moon is 7.36 × 1022 kg; The radius of the Moon is 1.74 × 106 m. The distance between the Earth and the Moon is 3.84 × 105 km.
Based on the above information answer the following questions:
(a) Write the distance between Earth and Moon (in ‘m’) in standard form.
(b) Write the mass of Earth in standard form.
(c) Write the product of mass of Moon and mass of Earth in exponential form.
Answer:
(a) 3.84 × 108 m
(B) 5.976 × 1024 kg
(c) 4.398 × 1029