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

Rajasthan Board RBSE Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.2 Textbook Exercise Questions and Answers.

RBSE Class 8 Maths Solutions Chapter 12 Exponents and Powers Ex 12.2

Question 1.
Express the following numbers in standard form:
(i) 0.0000000000085
Answer:
0.0000000000085 = \(\frac{85}{10000000000000}\)
= \(\frac{85}{10^{13}}=\frac{8.5 \times 10}{10^{13}}\)
= 8.5 × 10 × 10^-13
= 8.5 × 10^-12

(ii) 0.00000000000942
Answer:
0.00000000000942= \(\frac{942}{100000000000000}\)
= \(\frac{942}{10^{14}}=\frac{9.42 \times 100}{10^{14}}\)
= 9.42 × 10² × 10^-14
= 9.42 × 10^-12

(iii) 6020000000000000
Answer:
6020000000000000 = 602 × 10¹³
= 6.02 × 100 × 10¹³
= 6.02 × 10² × 10¹³
= 6.02 × 10¹⁵

(iv) 0.00000000837
Answer:
0.00000000837 = \(\frac{837}{100000000000}\)
= \(\frac{837}{10^{11}}=\frac{8.37 \times 100}{10^{11}}\)
= 8.37 × 10² × 10^-11
= 8.37 × 10^-9

(v) 31860000000
Answer:
31860000000= 3186 × 10⁷
= 3.186 × 10³ × 10⁷
= 3.186 × 10¹⁰

Question 2.
Express the following numbers in usual form:
(i) 3.02 × 10^-6
Answer:
3.02 × 10^-6 = \(\frac{302}{100} \times \frac{1}{10^{6}}=\frac{302}{100000000}\)
= 0.00000302

(ii) 4.5 × 10⁴
Answer:
4.5 × 10⁴ = \(\frac{45}{10}\) × 10⁴
= 45 × 10³ = 45000

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

(iv) 1.0001 × 10⁹
Answer:
1.0001 × 10⁹ = \(\frac{10001}{10000}\) × 10⁹= \(\frac{10001}{10^{4}}\) × 10⁹
= 10001 × 10⁵
= 1000100000

(v) 5.8 × 10¹²
Answer:
5.8 × 10¹² = \(\frac{58}{10}\) × 10¹²
= 5.8 × 10¹¹
= 580000000000

(vi) 3.61492 × 10⁶
Answer:
3.61492 × 10⁶ = \(\frac{361492}{100000}\) × 10⁶
= \(\frac{361492}{10^{5}}\) × 10⁶
= 361492 × 10
= 3614920

Question 3.
Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to \(\frac{1}{1000000}\) m
Answer:
1 micron \(\frac{1}{1000000}\) m = 1 × 10^-6 m

(ii) Charge of an electron is 0. 000,000,000,000,000,000,16 coulomb.
Answer:
Charge of an electron
= 0.00000000000000000016
= \(\frac{16}{100000000000000000000}\)
= \(\frac{16}{10^{20}}=\frac{1.6 \times 10}{10^{20}}=\frac{1.6}{10^{19}}\)
= 1.6 × 10^-19 coulomb

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

(iv) Size of a plant cell is 0.00001275 m
Answer:
Size of a plant cell
= 0.00001275 m
= \(\frac{1275}{100000000}\) m
= \(\frac{1.275 \times 1000}{10^{8}}\) m
= \(\frac{1.275 \times 10^{3}}{10^{8}}\) m = \(\frac{1.275}{10^{5}}\) m
= 1.275 × 10^-5 m

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

Question 4.
In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?
OR
In a heap there are five books each having thickness of 20 mm and there are five paper sheets each having thickness of 0.016 mm. Find the total thickness of the heap and express it in standard form.
Answer:
Thickness of one book = 20 mm
∴ Thickness of 5 books = 5 × 20 mm
= 100 mm

Thickness of one sheet of paper
= 0.016 mm

Thickness of 5 sheets of paper
= 5 × 0.016 mm
= 0.08 mm

Total thickness = 100 mm + 0.08 mm
= 100.08 mm
= 1.0008 × 10² mm