Question

1. calculate make the following conversions. express your answers in scientific notation. a. 14.8 g =? μg b. 3.72 g =? kg c. 66.3 l =? cm³ d. 7.5×10⁴ j =? kj e. 3.9×10⁵ mg =? dg f. 2.1×10⁻⁴ dl =? μl

Explanation:

Step1: Recall conversion factors

1 g = 10^6 μg, 1 kg = 1000 g, 1 L = 1000 cm^3, 1 kJ = 1000 J, 1 dg = 100 mg, 1 dL = 10^5 μL

Step2: Convert 14.8 g to μg

$14.8\ g\times10^{6}\frac{\mu g}{g}=1.48\times 10^{7}\ \mu g$

Step3: Convert 3.72 g to kg

$3.72\ g\times\frac{1\ kg}{1000\ g}=3.72\times 10^{- 3}\ kg$

Step4: Convert 66.3 L to cm^3

$66.3\ L\times1000\frac{cm^{3}}{L}=6.63\times 10^{4}\ cm^{3}$

Step5: Convert 7.5×10^4 J to kJ

$7.5\times 10^{4}\ J\times\frac{1\ kJ}{1000\ J}=75\ kJ = 7.5\times 10^{1}\ kJ$

Step6: Convert 3.9×10^5 mg to dg

$3.9\times 10^{5}\ mg\times\frac{1\ dg}{100\ mg}=3.9\times 10^{3}\ dg$

Step7: Convert 2.1×10^(-4) dL to μL

$2.1\times 10^{-4}\ dL\times10^{5}\frac{\mu L}{dL}=21\ \mu L=2.1\times 10^{1}\ \mu L$

Answer:

a. $1.48\times 10^{7}\ \mu g$
b. $3.72\times 10^{-3}\ kg$
c. $6.63\times 10^{4}\ cm^{3}$
d. $7.5\times 10^{1}\ kJ$
e. $3.9\times 10^{3}\ dg$
f. $2.1\times 10^{1}\ \mu L$