Class 8 - Mathematics
Exponents and Powers - Exercise 12.2
Top Block 1
1. Express the following numbers in standard form:
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000
Answer :
(i) 0.0000000000085
= 0.0000000000085 x 1012⁄1012
= 8.5 x 10-12
(ii) 0.00000000000942
= 0.00000000000942 x 1012⁄1012
= 9.42 x 10-12
(iii) 6020000000000000
= 6020000000000000 x 1012⁄1012
= 6.02 x 10-12
(iv) 0.00000000837
= 0.00000000837 x 1012⁄1012
= 8.37 x 10-12
(v) 31860000000 = 31860000000 x 1012⁄1012 = 3.186 x 10-12
2. Express the following numbers in usual form:
(i) 3.02 x 10-6
(ii) 4.5 x 104
(iii) 3 x 10-8
(iv) 1.0001 x 109
(v) 5.8 x 1012
(vi) 3.61492x 105
Answer :
(i) 3.02 x 10-6 = 3.02⁄106 = 0.00000302
(ii)4.5 x 104 = 4.5 x 10000 = 45000
(iii) 3 x 10-8 = 3⁄108 = 0.00000003
(iv) 1.0001 x 109 = 1000100000
(v) 5.8 x 1012 = 5.8 x 1000000000000 = 5800000000000
(vi) 3.61492x 105 = 3.61492 x 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 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.
Mddle block 1
Answer :
(i) 1 micron
1⁄1000000 = 1⁄106= 1 x 10-6 m
(ii)Charge of an electron is 0.00000000000000000016 coulombs.
= 0.00000000000000000016 x 1019⁄1019
= 1.6 x 10-19 coulomb
(iii) Size of bacteria = 0.0000005
= 5⁄10000000 = 5⁄107 = 5 x 10-7m
(iv) Size of a plant cell is 0.00001275 m
= 0.00001275 105⁄105 = 1.275 x 10-5 m
(v) Thickness of a thick paper = 0.07 mm
= 7⁄100 mm = 7⁄102 mm = 7 x 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?
Answer :
Thickness of one book = 20 mm
Thickness of 5 books = 20 x 5 = 100 mm
Thickness of one paper = 0.016 mm
Thickness of 5 papers = 0.016 x 5
= 0.08 mm
Total thickness of a stack = 100 + 0.08
=100.08 mm
= 100.08 x 102⁄102
1.0008 x 102 mm