Scientific notation Transitional Reasoning Practice

Questions

1. 1.

   In a classic surface chemistry experiment, a researcher prepares a compressed stearic acid monolayer on the water surface of a Langmuir trough. The resulting rectangular film has a length of $2.50 \times 10^1\text{ cm}$ and a width of $1.20 \times 10^1\text{ cm}$, and it contains a total of $1.50 \times 10^{17}$ closely packed molecules. Assuming the molecules form a continuous single layer without overlapping, what is the cross-sectional area occupied by a single stearic acid molecule in $\text{cm}^2$, expressed in standard scientific notation with the correct number of significant figures?

   • A) $2.00 \times 10^{-15}\text{ cm}^2$
   • B) $2.00 \times 10^{-16}\text{ cm}^2$
   • C) $2.00 \times 10^{-19}\text{ cm}^2$
   • D) $5.00 \times 10^{14}\text{ cm}^2$
2. 2.

   An analytical chemist tests a high-pressure liquid chromatography (HPLC) micro-injector by applying a force of $1.62 \times 10^1\text{ N}$ across a micro-piston with a contact area of $4.50 \times 10^{-5}\text{ m}^2$. Using the definition of pressure $P = \frac{F}{A}$, what is the pressure exerted on the fluid in pascals ($\text{N/m}^2$), expressed in standard scientific notation with the correct number of significant figures?

   • A) $3.60 \times 10^{-5}\text{ Pa}$
   • B) $3.60 \times 10^7\text{ Pa}$
   • C) $3.60 \times 10^5\text{ Pa}$
   • D) $3.60 \times 10^6\text{ Pa}$
3. 3.

   A microfluidics chemist fabricates a cylindrical capillary channel on a lab-on-a-chip device with a cross-sectional area of $4.50 \times 10^{-4}\text{ cm}^2$ and a length of $8.00 \times 10^1\text{ cm}$. The channel is filled entirely with an organic solvent that has a density of $7.50 \times 10^{-1}\text{ g/cm}^3$. Expressed in standard scientific notation with the correct number of significant figures, what is the total mass of the solvent contained within the channel?

   • A) $2.70 \times 10^{-2}\text{ g}$
   • B) $2.70 \times 10^{-1}\text{ g}$
   • C) $2.08 \times 10^1\text{ g}$
   • D) $2.70 \times 10^{-3}\text{ g}$
4. 4.

   An environmental chemist monitors sulfur dioxide emissions from an industrial exhaust stack. Over a testing duration of $2.50 \times 10^3\text{ minutes}$, the facility discharges a total of $4.80 \times 10^5\text{ mg}$ of sulfur dioxide. Expressed in standard scientific notation with the correct number of significant figures, what is the average emission rate of sulfur dioxide in grams per second ($\text{g/s}$)?

   • A) $3.20 \times 10^{-3}\text{ g/s}$
   • B) $3.20 \times 10^0\text{ g/s}$
   • C) $1.92 \times 10^{-1}\text{ g/s}$
   • D) $3.20 \times 10^3\text{ g/s}$
5. 5.

   A surface chemist synthesizes uniform cubic platinum nanocubes to serve as catalysts in fuel cells. High-resolution electron microscopy establishes that each nanocube has an edge length of $4.0 \times 10^{-7}\text{ cm}$. Using the geometric formula $V = l^3$, what is the volume of a single nanocube in cubic centimeters ($\text{cm}^3$), expressed in standard scientific notation?

   • A) $6.4 \times 10^{-22}\text{ cm}^3$
   • B) $1.2 \times 10^{-20}\text{ cm}^3$
   • C) $64 \times 10^{-21}\text{ cm}^3$
   • D) $6.4 \times 10^{-20}\text{ cm}^3$
6. 6.

   A pharmaceutical chemist designs a targeted drug-delivery carrier using spherical lipid vesicles. Quality-control testing establishes that each vesicle encapsulates an average of $6.0 \times 10^3$ drug molecules, and the mass of a single drug molecule is $5.5 \times 10^{-22}\text{ g}$. If a single therapeutic injection administers $2.0 \times 10^{11}$ vesicles, what is the total mass of the active drug delivered in the injection, expressed in standard scientific notation?

   • A) $6.6 \times 10^{-7}\text{ g}$
   • B) $6.6 \times 10^{-8}\text{ g}$
   • C) $6.6 \times 10^{-6}\text{ g}$
   • D) $66 \times 10^{-8}\text{ g}$
7. 7.

   An analytical chemist combines two separate atmospheric particulate samples collected on air-monitoring filters to evaluate total airborne contamination. Filter 1 contains a collected mass of $1.75 \times 10^{-3}\text{ g}$, and Filter 2 contains a collected mass of $8.2 \times 10^{-4}\text{ g}$. Expressed in standard scientific notation with the correct number of significant figures, what is the total combined mass of the particulate matter?

   • A) $2.57 \times 10^{-3}\text{ g}$
   • B) $9.95 \times 10^{-3}\text{ g}$
   • C) $2.57 \times 10^{-7}\text{ g}$
   • D) $1.83 \times 10^{-3}\text{ g}$
8. 8.

   A materials chemist synthesizes a batch of uniform silica nanoparticles for targeted drug delivery. The total mass of the collected nanoparticles is $1.44 \times 10^{-2}\text{ g}$, and particle tracking analysis determines that the sample contains $4.50 \times 10^{16}$ nanoparticles. To find the average mass of an individual nanoparticle, the chemist divides the total sample mass by the number of particles. Expressed in standard scientific notation with the correct number of significant figures, what is the average mass of a single nanoparticle in grams?

   • A) $3.20 \times 10^{-17}\text{ g}$
   • B) $3.20 \times 10^{14}\text{ g}$
   • C) $0.320 \times 10^{-18}\text{ g}$
   • D) $3.20 \times 10^{-19}\text{ g}$
9. 9.

   An environmental chemist analyzing zinc oxide nanoparticles in an urban water runoff sample records an average particle diameter of 0.0000450 mm using transmission electron microscopy. For international reporting, the chemist must express this value in standard scientific notation in meters (m) without altering the number of significant figures. Which expression correctly represents the nanoparticle diameter in meters?

   • A) $4.5 \times 10^{-8}\text{ m}$
   • B) $45.0 \times 10^{-9}\text{ m}$
   • C) $4.50 \times 10^{-5}\text{ m}$
   • D) $4.50 \times 10^{-8}\text{ m}$

Answers and step-by-step solutions appear after you finish the test.