Answer
a) 1.28 km
b) 3.18$\times$$10^{-3}$mg
c) 8.14$\times$$10^{7}$dm
e) 3.8 m/s
Work Step by Step
a) 7.310 km$\div$5.70 km
Simply divide 7.310 km$\div$5.70 km = 1.28245614 km
since the 5.70 has the lower number of significant figures that is 3 sig figs the answer should be reported to 3 significant figures the answer will be 1.28 km
b) (3.26$\times$$10^{-3}$mg)-(7.88$\times$$10^{-5}$mg)
In doing subtraction or addition of scientific notation the exponents must have the same numbers thus,
3.26$\times$$10^{-3}$ = 3.26$\times$$10^{-3}$
7.88$\times$$10^{-5}$ = 0.0788$\times$$10^{-3}$
(3.26$\times$$10^{-3}$ mg)-(0.0788$\times$$10^{-3}$ mg)=3.1812$\times$$10^{-3}$ mg
since the both terms has 3 sig figs, the answer must be reported to 3 sig figs that is 3.18$\times$$10^{-3}$ mg
c) (4.02$\times$$10^{6}$ dm)+(7.74$\times$$10^{7}$ dm)
Again the same procedure from number letter b applies to letter c
4.02$\times$$10^{6}$ = 0.0402$\times$$10^{7}$
7.74$\times$$10^{7}$ = 7.74$\times$$10^{7}$
(0.0402$\times$$10^{7}$ dm)+(7.74$\times$$10^{7}$ dm)=8.14$\times$$10^{7}$dm
If you get this answer, 81420000 simply convert it to scientific notation and report to 3 sig figs
d) $\frac{(7.8m-0.34m)}{(1.15s+0.82s)}$
In doing chain calculations, simplify first the numerator and the denominator and report them to the correct sig figs
(7.8m-0.34m)=7.5m
(1.15s+0.82s)=2.0s
$\frac{(7.5m)}{(2.0s)}$=3.75 m/s
since both terms have 2 sig figs the answer must be reported to 2 sig figs thus, the answer is 3.8 m/s
