Question

a) how many centimeters are in 1 kilometer?
b) how many megaseconds are in 1 nanosecond?
c) how many femtometers are in 1 terameter?
d) how many deciliters are in 5.3 microlitres?
e) how many milligrams are in 5.25 gigagrams?
f) how many kilowatts are in 81.3 milliwatts?

Explanation:

Step1: Recall length - unit conversion factor

1 km = 1000 m and 1 m=100 cm, so 1 km = 1000×100 cm.
1 km = 100000 cm

Step2: Recall time - unit conversion factor

1 s = 10^6 ms and 1 s = 10^9 ns, so 1 ns=10^(- 9) s and 1 Ms = 10^6 s. Then 1 ns = 10^(-9)/10^6 Ms=10^(-15) Ms

Step3: Recall length - unit conversion factor

1 Tm = 10^12 m and 1 m = 10^15 fm, so 1 Tm=10^12×10^15 fm = 10^27 fm

Step4: Recall volume - unit conversion factor

1 dL = 0.1 L and 1 μL=10^(-6) L. So 5.3 μL = 5.3×10^(-6) L. Then 5.3 μL=(5.3×10^(-6)/0.1) dL = 5.3×10^(-5) dL

Step5: Recall mass - unit conversion factor

1 g = 1000 mg and 1 Gg = 10^9 g. So 5.25 Gg=5.25×10^9 g. Then 5.25 Gg = 5.25×10^9×1000 mg=5.25×10^12 mg

Step6: Recall power - unit conversion factor

1 kW = 1000 W and 1 mW = 10^(-3) W. So 81.3 mW = 81.3×10^(-3) W. Then 81.3 mW=(81.3×10^(-3)/1000) kW=8.13×10^(-5) kW

Answer:

a) 100000
b) 10^(-15)
c) 10^27
d) 5.3×10^(-5)
e) 5.25×10^12
f) 8.13×10^(-5)