1. Express the following numbers in standard form.
(i) 0.0000000000085
Solution:
= 0.0000000000085×(1012/1012) = 8.5 ×10-12
(ii) 0.00000000000942
Solution:
= 0.00000000000942×(1012/1012) = 9.42×10-12
(iii) 6020000000000000
Solution:
= 6020000000000000×(1015/1015) = 6.02×1015
(iv) 0.00000000837
Solution:
= 0.00000000837×(109/109) = 8.37×10-9
(v) 31860000000
Solution:
= 31860000000×(1010/1010) = 3.186×1010
2.Express the following numbers in usual form.
(i) 3.02×10-6
Solution:
= 3.02/106 = 0 .00000302
(ii) 4.5×104
Solution:
= 4.5×10000 = 45000
(iii)3×10-8
Solution:
= 3/108 = 0.00000003
(iv)1.0001×109
Solution:
= 1000100000
(v) 5.8×1012
Solution:
= 5.8×1000000000000 = 5800000000000
(vi)3.61492×106
Solution:
= 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.
Solution:
1 micron = 1/1000000
= 1/106
= 1×10-6
(ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 Coulomb.
Solution:
= 0.00000000000000000016×1019/1019
= 1.6×10-19 coulomb
(iii) Size of bacteria is 0.0000005 m
Solution:
= 5/10000000
= 5/107 = 5×10-7 m
(iv) Size of a plant cell is 0.00001275 m
Solution:
= 0.00001275×105/105
= 1.275×10-5m
(v) Thickness of a thick paper is 0.07 mm
Solution:
= 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 x 102 mm
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