RS Aggarwal Solutions: Exercise 2B - Exponents

Q.1. Write each of the following numbers in standard form:

(i) 57.36

(ii) 3500000

(iii) 273000

(iv) 168000000

(v) 4630000000000

(vi) 345 × 10⁵
Ans.
(i) 57.36 = 5.736 × 10
(ii) 3500000 = 3.5 × 10⁶
(iii) 273000 = 2.73×10⁵
(iv) 168000000 = 1.68 × 10⁸
(v) 4630000000000=4.63 × 10¹²
(vi) 345 × 10⁵ = 3.45 × 10⁷

Q.2. Write each of the following numbers in usual form:

(i) 3.74 × 10⁵

(ii) 6.912 × 10⁸

(iii) 4.1253 × 10⁷

(iv) 2.5 × 10⁴

(v) 5.17 × 10⁶

(vi) 1.679 × 10⁹
Ans.
(i)

(ii)

(iii)

(iv)

(v)

(vi)


Q.3. (i) The height of Mount Everest is 8848 m. Write it in standard form.

(ii) The speed of light is 300000000 m/sec. Express it in standard form.

(iii) The distance from the earth to the sun is 149600000000 m. Write it in standard form.
Ans.
(i) The height of the Mount Everest is 8848 m.

In standard form, we have:
8848=8.848×1000 m=8.848×10³m.
(ii) The speed of light is 300000000 m/s.

In standard form, we have: 

300000000=3×100000000 m/s=3×10⁸ m/s

(iii) The Sun-Earth distance is 149600000000 m.

In standard form, we have: 149600000000=1496×100000000=1.496×1000×100000000=1.496×10³×10⁸ = 1.496×10¹¹m

Q.4. Mass of earth is (5.97 × 10²⁴) kg and mass of moon is (7.35 × 10²²) kg. What is the total mass of the two?
Ans.
Mass of the Earth = 5.97×10²⁴ kg
Now, 5.97×10²⁴=5.97×10⁽²⁺²²⁾=5.97×10²×10²²=597×10²²

So, the mass of the Earth can also be written as 597×10²² kg.
Mass of the Moon = 7.35×10²² kg
Sum of the masses of the Earth and the Moon:=(597×10²²)+(7.35×10²²)

(597+7.35)×10²²=604.35×10²² kg
=6.0435×100×10²² =6.0435 × 10² × 10²² = 6.0435×10⁽²⁺²²⁾ = 6.0435×10²⁴ kg

Q.5. Write each of the following numbers in standard form:
(i) 0.0006
(ii) 0.00000083
(iii) 0.0000000534
(iv) 0.0027
(v) 0.00000165
(vi) 0.00000000689
Ans.
(i)

(ii)

(iii)


(iv)

(v)

(vi)

Q.6.
(i) 1 micron = m. Express it in standard form.

(ii) Size of a bacteria = 0.0000004 m. Express it in standard form.

(iii) Thickness of a paper = 0.03 mm. Express it in standard form.
Ans.
(i) 1 micron = m=1×10^-6 m
(ii) 0.0000004 m =
(iii) Thickness of paper = 0.03 mm = (3×10^-2) mm

Q.7. Write each of the following numbers in usual form:

(i) 2.06 × 10^-5

(ii) 5 × 10-7

(iii) 6.82 × 10-6

(iv) 5.673 × 10-4

(v) 1.8 × 10-2

(vi) 4.129 × 10-3
Ans.
(i)

(ii)

(iii)

(iv)

(v)

(vi)