NCERT Solutions Class 8 Mathematics Chapter 12 Exponents And Powers

Exercise 12.1

Q.1) Evaluate:
i) 3−2 ii) (−4)−2 iii) (1/5) −5
Sol.1)

= 3⁻⁵⁺⁵ × 2⁻⁵⁺⁵ × 5⁻²⁺⁷ = 3⁰ × 2⁰ × 5⁵
= 1 × 1 × 3125 = 3125

Exercise 12.2

Q.1) Express the following numbers in standard form:
(i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000
(iv) 0.00000000837 (v) 31860000000
Sol.1)

Q.2) Express the following numbers in usual form:
i) 3.02 × 10⁻⁶ ii) 4.5 × 10⁴ iii) 3 × 10⁻⁴ iv) 1.0001 × 10⁹
v) 5.8 × 10¹² vi) 3.61492 × 10⁶
Sol.2) i) 3.02 × 10⁻⁶
= 3.02/106 = 0.00000302
ii) 4.5 × 10⁴
= 4.5 × 10000 = 45000
iii) 3 × 10⁻⁴ = 3/10⁸
= 0.00000003
iv) 1.0001 × 10⁹ 
= 100100000
v) 5.8 × 10¹² 
= 5.8 × 1000000000000 = 5800000000000
vi) 3.61492 × 10⁶ 
= 3.61492 × 1000000 = 3614920

Q.3)` Express the number appearing in the following statements in standard form:
(i) 1 micron is equal to (1/1000000( m.
(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
(iii) Size of a bacteria is 0.0000005 m.
(iv) Size of a plant cell is 0.00001275 m.
(v) Thickness if a thick paper is 0.07 mm.
Sol.3) i) 1 micron = 1/1000000 = 1/106 = 1 × 10⁶𝑚
(ii) Charge of an electron is 0.00000000000000000016 coulombs. = 0.00000000000000000016 × 1019/1019 = 1.6 × 10⁻¹⁹ coulombs.
(iii) Size of a bacteria is 0.0000005 m.
= 5/10000000 = 5/107 = 5 × 10⁻⁷𝑚
(iv) Size of a plant cell is 0.00001275 m.
= 0.00001275 × 105/105 = 1.275 × 10⁻⁵𝑚
(v) Thickness if a thick paper is 0.07 mm.
= 7/100 𝑚𝑚 = 7/102 = 7 × 10⁻²𝑚𝑚

Q.4) In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?
Sol.4) Thickness of one book = 20 mm
Thickness of 5 books = 20 × 5 = 100 𝑚𝑚
Thickness of one paper = 0.016 mm
Thickness of 5 papers = 0.016 × 5 = 0.08 𝑚𝑚
Total thickness of a stack = 100 + 0.08
= 100.08 𝑚𝑚 = 100.08 × 102/102 = 1.0008 × 10² 𝑚𝑚