Question

make the following conversions. express your answers in scientific notation.
a. 14.8 g to μg
14.8g. $\frac{10^{3}mu g}{1g}=$
b. 3.72 x 10⁻³ kg to grams
c. 66.3 l to cm³
d. 7.5 x 10⁴ j to kj
e. 3.9 x 10⁵ mg to dg
f. 2.21 x 10⁴ dl to μl

Explanation:

Step1: Recall conversion factor for g to μg

1 g = 10⁶ μg. So, 14.8 g×$\frac{10^{6}\text{ }\mu\text{g}}{1\text{ g}}=1.48\times 10^{7}\text{ }\mu\text{g}$

Step2: Recall conversion factor for kg to g

1 kg = 1000 g. So, $3.72\times 10^{-3}\text{ kg}\times\frac{10^{3}\text{ g}}{1\text{ kg}} = 3.72\text{ g}=3.72\times 10^{0}\text{ g}$

Step3: Recall conversion factor for L to cm³

1 L = 1000 cm³. So, 66.3 L×$\frac{10^{3}\text{ cm}^{3}}{1\text{ L}}=6.63\times 10^{4}\text{ cm}^{3}$

Step4: Recall conversion factor for J to kJ

1 kJ = 1000 J. So, $7.5\times 10^{4}\text{ J}\times\frac{1\text{ kJ}}{10^{3}\text{ J}} = 75\text{ kJ}=7.5\times 10^{1}\text{ kJ}$

Step5: Recall conversion factor for mg to dg

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

Step6: Recall conversion factor for dL to μL

1 dL = 100000 μL. So, $2.21\times 10^{-4}\text{ dL}\times\frac{10^{5}\text{ }\mu\text{L}}{1\text{ dL}} = 22.1\text{ }\mu\text{L}=2.21\times 10^{1}\text{ }\mu\text{L}$

Answer:

a. $1.48\times 10^{7}\text{ }\mu\text{g}$
b. $3.72\times 10^{0}\text{ g}$
c. $6.63\times 10^{4}\text{ cm}^{3}$
d. $7.5\times 10^{1}\text{ kJ}$
e. $3.9\times 10^{3}\text{ dg}$
f. $2.21\times 10^{1}\text{ }\mu\text{L}$