Q71E
Question
Use scientific (exponential) notation to express the following quantities in terms of the SI base units in Table1.3:
(a) 0.13 g
(b) 232 Gg
(c) 5.23 pm
(d) 86.3 mg
(e) 37.6 cm
(f) 54 μm
(g) 1 Ts
(h) 27 ps
(i) 0.15 mK
Step-by-Step Solution
Verified(a) 1.310-4 kg
(b) 2.32 108 kg
(c) 5.23 10-12 m
(d) 8.63 10-5 kg
(e) 0.376 m
(f) 5.4 10-5m
(g) 1 1012 s
(h) 2.7 10-11 s
(i) 1.5 10-4 K
The SI units are the standard units based on the international system of units. The following figure shows the basic SI units of the physical quantities. There are only seven basic SI units used by many international institutes.
The measures are seconds for time, Kelvin for temperature, a mole for amount, meter for length, kilogram for mass, Candela for luminous intensity, and Ampere for current.
Here we will convert the given units of the quantities into SI units by using data from Table 1.3. The following quantities are converted as
(a) 0.13 g
\(0.13\,\,g\,\, = \,\,0.13\, \times \,\frac{{{{10}^{ - 3}}}}{{{{10}^{ - 3}}}}\,g\,\, = \,\,0.13\,\, \times \,\,{10^{ - 3}}\,\,kg\,\, = \,\,1.3\, \times \,{10^{ - 4}}\,\,kg\)
(b) 232 Gg
\(232\,\,Gg\,\, = \,\,232\,\, \times \,\,{10^9}\,g\,\, = \,\,232\,\, \times \,\,{10^6}\,\,({10^3}\,g)\,\, = \,232\,\, \times \,\,{10^6}\,kg\, = \,\,2.32\,\, \times \,\,{10^8}\,kg\)
(c) 5.23 pm
\(5.23\,\,pm\,\, = \,\,5.23\,\, \times \,\,{10^{ - 12}}\,\,m\,\,\)
(d) 86.3 mg
\(86.3\,\,mg\,\, = \,\,86.3\,\, \times \,\,{10^{ - 3}}\,\,g\, = \,86.3\,\, \times \,\,{10^{ - 3}}\, \times \frac{{{{10}^{ - 3}}}}{{{{10}^{ - 3}}}}\,g\,\, = \,\,86.3\,\, \times \,\,{10^{ - 6}}\,\,kg\,\,\, = \,\,8.63\,\, \times \,\,{10^{ - 5}}\,\,kg\)
(e) 37.6 cm
\(37.6\,\,cm\,\, = \,\,37.6\,\, \times \,\,{10^{ - 2}}\,\,m\,\, = \,\,0.376\,\,m\)
(f) 54
\(54\,\,\mu m\,\, = \,\,54\,\, \times \,\,{10^{ - 6}}\,m\)
(g) 1 Ts
\(1\,\,Ts\,\, = \,\,1\,\, \times \,\,{10^{12}}\,s\)
(h) 27 ps
\(27\,\,ps\,\, = \,\,27\,\, \times \,\,{10^{ - 12}}\,s\,\, = \,\,2.7\,\, \times \,\,{10^{ - 11}}\,\,s\).
(i) 0.15 mK
\(0.15\,mK\,\, = \,\,0.15\,\, \times \,\,{10^{ - 3}}\,\,K\,\, = \,\,1.5\,\, \times \,\,{10^{ - 4}}\,K\)