Class 8 | NCERT Solution Maths Chapter 12 | Exponents and Powers | Exercise 12.2

Exercise 12.2 Page No: 200

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

Solution:

(i) 0.0000000000085 = 0.0000000000085×(1012/1012) = 8.5 ×10-12

(ii) 0.00000000000942 = 0.00000000000942×(1012/1012) = 9.42×10-12

(iii) 6020000000000000 = 6020000000000000×(1015/1015) = 6.02×1015

(iv) 0.00000000837 = 0.00000000837×(109/109) = 8.37×10-9

(v) 31860000000 = 31860000000×(1010/1010) = 3.186×1010

2.Express the following numbers in usual form.
(i) 3.02×10-6
(ii) 4.5×104
(iii)3×10-8
(iv)1.0001×109
(v) 5.8×1012
(vi)3.61492×106

Solution:

(i) 3.02×10-6 = 3.02/106 = 0 .00000302

(ii) 4.5×104 = 4.5×10000 = 45000

(iii) 3×10-8 = 3/108 = 0.00000003

(iv) 1.0001×109 = 1000100000

(v) 5.8×1012 = 5.8×1000000000000 = 5800000000000

(vi) 3.61492×106 = 3.61492×1000000 = 3614920

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 bacteria is 0.0000005 m
(iv)  Size of a plant cell is 0.00001275 m
(v) Thickness of a thick paper is 0.07 mm

Solution :

(i) 1 micron = 1/1000000

= 1/106

= 1×10-6

(ii) Charge of an electron is 0.00000000000000000016 coulombs.

= 0.00000000000000000016×1019/1019

= 1.6×10-19 coulomb

(iii) Size of bacteria = 0.0000005

=  5/10000000 = 5/107 = 5×10-7 m

(iv) Size of a plant cell is 0.00001275 m

= 0.00001275×105/105

= 1.275×10-5m

(v) Thickness of a thick paper = 0.07 mm

0.07 mm = 7/100 mm = 7/102 = 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 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 mm

=1.0008 ×102 mm