Use scientific (exponential) notation to express the following quantities in terms of the si base units in table 1.3 :
(a) 0.13 g
(b) 232 gg
(c) 5.23 pm
(d) 86.3 mg
(e) 37.6 cm
(f) 54
(g) 1 ts
(h) 27 ps
(i) 0.15 mk

a) 0.13 g = 0.13X0.001 kg = 1.3 X 10⁻⁴ kg

b) 232 Gg = 232 X  1000000 kg = 2.32 X 10⁸ kg

c) 5.23 pm = 5.23 X 10⁻¹² m

d) 86.3 mg = 86.3 X 10⁻⁶Kg = 8.63 X 10⁻⁵Kg

e) 37.6 cm = 37.6 X 10⁻² m = 3.76 X 10⁻¹m

f) 54 = 5.4 X 10¹

g) 1 Ts = 10¹² seconds

h ) 27 ps = 27 X 10⁻¹² s= 2.7 X 10⁻¹¹ s

i) 0.15 mK = 1.5 X10⁻⁴ K

Explanation:

A scientific notation is a representation of any number which is very large or very small. It is simplification of writing a number.

The SI units of

i) weight = Kg

ii) length = meter

iii) time = second

iv) temperature = K

a) 0.13 g = 0.13X0.001 kg = 1.3 X 10⁻⁴ kg

b) 232Gg

1 Gg = 1000000 kg

232 Gg = 232 X  1000000 kg = 2.32 X 10⁸ kg

c) 5.23 pm

1 pm = 10⁻¹² m

5.23 pm = 5.23 X 10⁻¹² m

d) 86.3 mg

1mg = 10⁻⁶Kg

86.3 mg = 86.3 X 10⁻⁶Kg = 8.63 X 10⁻⁵Kg

e) 37.6cm

1 cm = 10⁻² m

37.6 cm = 37.6 X 10⁻² m = 3.76 X 10⁻¹m

f) 54 (no units)

54 = 5.4 X 10¹

g) 1 Ts = 10¹² seconds

h ) 27 ps

1 ps = 10⁻¹² s

27 ps = 27 X 10⁻¹² s= 2.7 X 10⁻¹¹ s

i) 0.15 mK

1mK = 10⁻³ K

0.15 mK = 1.5 X10⁻⁴ K