PSEB 8th Class Maths Solutions Chapter 12 Exponents and Powers Ex 12.2

Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 12 Exponents and Powers Ex 12.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.2

1. Express the following numbers in standard form:

Question (i)
0.0000000000085
Solution:
= \(\frac{85}{10000000000000}\)
= \(\frac{85}{10^{13}}\)
= \(\frac{8.5 \times 10}{10^{13}}\)
= 8.5 × 10 × 10^-13
= 8.5 × 10^-12

Question (ii)
0.00000000000942
Solution:
= \(\frac{942}{100000000000000}\)
= \(\frac{942}{10^{14}}\)
= \(\frac{9.42 \times 10^{2}}{10^{14}}\)
= 9.42 × 10² × 10^-14
= 9.42 × 10^-12

Question (iii)
6020000000000000
Solution:
= 602 × 10000000000000
= 602 × 10¹³
= 6.02 × 10² × 10¹³
= 6.02 × 10¹⁵

Question (iv)
0.00000000837
Solution:
= \(\frac{837}{100000000000}\)
= \(\frac{837}{10^{11}}\)
= \(\frac{8.37 \times 10^{2}}{10^{11}}\)
= 8.37 × 10² × 10^-11
= 8.37 × 10^2+(-11)
= 8.37 × 10^-9

Question (v)
31860000000
Solution:
= 3186 × 10000000
= 3186 × 10⁷
= 3.186 × 10³ × 10⁷
= 3.186 × 10^{3 + 7}
= 3.186 × 10¹⁰

2. Express the following numbers in usual form:

Question (i)
3.02 × 10^-6
Solution:
= 302 × 10^-2 × 10^-6
= 302 × 10^-8
= \(\frac{302}{100000000}\)
= 0.00000302

Question (ii)
4.5 × 10⁴
Solution:
= \(\frac {45}{10}\) × 10000
= 45 × 1000
= 45000

Question (iii)
3 × 10^-8
Solution:
= \(\frac{3}{100000000}\)
= 0.00000003

Question (iv)
1.0001 × 10⁹
Solution:
= \(\frac{10001}{10000}\) × 1000000000
= 10001 × 100000
= 1000100000

Question (v)
5.8 × 10¹²
Solution:
= \(\frac {58}{10}\) × 100000000000
= 58 × 10000000000
= 5800000000000

Question (vi)
3.61492 × 10⁶
Solution:
= \(\frac{361492}{100000}\) × 1000000
= 361492 x 10
= 3614920

3. Express the number appearing in the following statements in standard form:

Question (i)
1 micron is equal to \(\frac{1}{1000000}\) m.
Solution:
1 micron = \(\frac{1}{1000000}\)m
= \(\frac{1}{10^{6}}\)m
∴ 1 micron = 1 × 10^-6 m

Question (ii)
Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
Solution:
Charge of an electron
= 0.000,000,000,000,000,000,16 coulomb
= \(\frac{16}{100000000000000000000}\) coulomb
= \(\frac{1.6 \times 10}{10^{20}}\) coulomb
= \(\frac{1.6}{10^{19}}\) coulomb
= 1.6 × 10^-19 coulomb
∴ Charge of an electron = 1.6 × 10^-19 coulomb

Question (iii)
Size of a bacteria is 0.0000005 m.
Solution:
Size of a bacteria = 0.0000005 m
= \(\frac{5}{10000000}\)m
= \(\frac{5}{10^{7}}\)m
= 5 × 10^-7 m
∴ Size of a bacteria = 5 × 10^-7 m

Question (iv)
Size of a plant cell is 0.00001275 m.
Solution:
Size of a plant cell = 0.00001275 m
= \(\frac{1275}{100000000}\)m
= \(\frac{1275}{10^{8}}\)m
= \(\frac{1.275 \times 10^{3}}{10^{8}}\) m
= 1.275 × 10^3-8
= 1.275 × 10^-5
∴ Size of a plant cell
= 1.275 × 10^-5 m

Question (v)
Thickness of a thick paper is 0.07 mm.
Solution:
Thickness of a thick paper = 0.07 mm
= \(\frac {7}{100}\) mm
= \(\frac{7}{10^{2}}\) mm
= 7 × 10^-2 mm
∴ Thickness of a thick paper
= 7 × 10^-2 mm

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.
Solution:
Thickness of a book = 20 mm
∴ Thickness of 5 books = (5 × 20) mm
= 100 mm
Thickness of a paper sheet = 0.016 mm
∴ Thickness of 5 paper sheets
= (5 × 0.016) mm
= 0.08 mm
∴ Total thickness of a stack = Thickness of books + Thickness of paper sheets
= (100 + 0.08) mm
= 100.08 mm
In standard form 100.08 is written as 1.0008 × 10².
Thus, the total thickness of the stack is 1.0008 × 10² mm.