Welcome to the world of Exponents and Powers, where numbers reach new heights and mathematics takes on a whole new dimension! Exponents are like shortcuts in math; they help us write and calculate large numbers more efficiently. For example, instead of writing 2 multiplied by itself four times as 2 x 2 x 2 x 2, we can simply write 2 to the power of 4, which is 2⁴.
Imagine if you had to count all the stars in the sky – a nearly impossible task! With exponents, it’s a bit like having a superpower to count them quickly. If a scientist says there are 10⁶ stars in a small region of space, that exponent tells you it’s a 1 followed by six zeros: 1,000,000!
In this chapter, we’ll explore how to multiply numbers by themselves using exponents, and how to make really big or really small numbers easier to work with through the power of powers. You’ll learn the language of the universe as you work with numbers that describe everything from the tiniest atoms to the vastness of galaxies. So let’s power up and dive into the exhilarating universe of exponents and powers!
NCERT Question and Answers for Class 7 Maths Exercise 11.3 Chapter 11 Exponents and Powers
1. Write the following numbers in the expanded forms:
Solution:
279404 =
2 × 100000 + 7 × 10000 + 9 × 1000 + 4 × 100 + 0 × 10 + 4 × 1
= 200000 + 70000 + 9000 + 400 + 0 + 4
3006194 =
3 × 1000000 + 0 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 4 × 1
= 3000000 + 0 + 0 + 6000 + 100 + 90 + 4
2806196 =
2 × 1000000 + 8 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 6 × 1
= 2000000 + 800000 + 0 + 6000 + 100 + 90 + 6
120719 =
1 × 100000 + 2 × 10000 + 0 × 1000 + 7 × 100 + 1 × 10 + 9 × 1
= 100000 + 20000 + 0 + 700 + 10 + 9
20068 =
2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8 × 1
= 20000 + 0 + 0 + 60 + 8
2. Find the number from each of the following expanded forms:
Solution:
(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰
= 80000 + 6000 + 0 + 40 + 5
= 86045
(b) 4 × 10⁵ + 5 × 10³ + 3 × 10² + 2 × 10⁰
= 400000 + 5000 + 300 + 2
= 405302
(c) 3 × 10⁴ + 7 × 10² + 5 × 10⁰
= 30000 + 700 + 5
= 30705
(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹
= 900000 + 200 + 30
= 900230
3. Express the following numbers in standard form:
(i) 5,00,00,000
5 x 10⁷
(ii) 70,00,000
7 x 10⁶
(iii) 3,18,65,00,000
3.1865 x 10¹⁰
(iv) 3,90,878
3.90878 x 10⁵
(v) 39087.8
3.90878 x 10⁴
(vi) 3908.78
3.90878 x 10³
4. Express the number appearing in the following statements in standard form:
(a) The distance between Earth and Moon is 384,000,000 m
3.84 x 10⁸ m.
(b) Speed of light in vacuum is 300,000,000 m/s
3 x 10⁸ m/s.
(c) Diameter of the Earth is 1,27,56,000 m
1.2756 x 10⁷ m.
(d) Diameter of the Sun is 1,400,000,000 m
1.4 x 10⁹ m.
(e) In a galaxy there are on average 100,000,000,000 stars
1 x 10¹¹ stars.
(f) The universe is estimated to be about 12,000,000,000 years old
1.2 x 10¹⁰ years.
(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m
3 x 10²⁰ m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm
6.023 x 10²³ molecules.
(i) The earth has 1,353,000,000 cubic km of sea water
1.353 x 10⁹ cubic km.
(j) The population of India was about 1,027,000,000 in March, 2001
1.027 x 10⁹.
Additional Question and Answers for Exercise 11.3 Exponents and Powers
1. Write the following numbers in the expanded forms:
(i) 9475064
9 × 10⁶ + 4 × 10⁵ + 7 × 10⁴ + 5 × 10³ + 0 × 10² + 6 × 10¹ + 4 × 10⁰
(ii) 82039005
8 × 10⁷ + 2 × 10⁶ + 0 × 10⁵ + 3 × 10⁴ + 9 × 10³ + 0 × 10² + 0 × 10¹ + 5 × 10⁰
(iii) 7601203
7 × 10⁶ + 6 × 10⁵ + 0 × 10⁴ + 1 × 10³ + 2 × 10² + 0 × 10¹ + 3 × 10⁰
2. Find the number from each of the following expanded forms:
(a) 7 × 10⁵ + 2 × 10⁴ + 9 × 10³ + 8 × 10² + 6 × 10¹ + 1 × 10⁰
7209861
(b) 3 × 10⁶ + 0 × 10⁵ + 0 × 10⁴ + 5 × 10³ + 1 × 10² + 4 × 10¹
3000514
(c) 6 × 10⁶ + 0 × 10⁵ + 4 × 10⁴ + 0 × 10³ + 7 × 10² + 2 × 10¹
6040072
3. Express the following numbers in standard form:
(i) 987000000
9.87 x 10⁸
(ii) 54000000
5.4 x 10⁷
Worksheet Exercise 11.3 Exponents and Powers
1. Write the following numbers in the expanded forms:
(a) 8642051
(b) 7201398
(c) 9531000
(d) 481216
(e) 650203
(f) 39102007
2. Find the number from each of the following expanded forms:
(a) 3 × 10⁶ + 2 × 10⁵ + 6 × 10⁴ + 4 × 10³ + 0 × 10² + 1 × 10¹ + 5 × 10⁰
(b) 4 × 10⁵ + 7 × 10⁴ + 1 × 10³ + 3 × 10² + 9 × 10¹ + 0 × 10⁰
(c) 9 × 10⁶ + 0 × 10⁵ + 0 × 10⁴ + 0 × 10³ + 3 × 10² + 2 × 10¹ + 8 × 10⁰
(d) 1 × 10⁷ + 2 × 10⁶ + 0 × 10⁵ + 4 × 10⁴ + 0 × 10³ + 0 × 10² + 0 × 10¹ + 6 × 10⁰
(e) 5 × 10⁵ + 6 × 10⁴ + 2 × 10³ + 0 × 10² + 8 × 10¹ + 7 × 10⁰
(f) 8 × 10⁶ + 0 × 10⁵ + 3 × 10⁴ + 1 × 10³ + 5 × 10² + 9 × 10¹ + 0 × 10⁰
3. Express the following numbers in standard form:
(a) 876000000
(b) 65000000
(c) 21000000000
(d) 504000
(e) 30010.5
(f) 7200.92
4. Express the number appearing in the following statements in standard form.
(a) The total human DNA base pairs are approximately 3,200,000,000.
(b) The Andromeda Galaxy is approximately 2,537,000,000,000,000,000 km from Earth.
(c) The observable universe is about 880,000,000,000,000,000,000,000 km in diameter.
(d) The average human heart beats about 115,000 times in one day.
(e) The number of grains of sand on Earth’s beaches is roughly 7,500,000,000,000,000,000.
(f) The estimated number of stars in the Milky Way is about 400,000,000,000.
