Scientific notation Transitional Reasoning Download PDF

Questions

1. 1.

   During an oceanographic survey, an echo sounder on a research vessel emits an acoustic pulse downward toward the seabed. The pulse travels through seawater at an average speed of $1.5 \times 10^3$ m/s and the reflected echo is detected back at the vessel $4.8 \times 10^{-2}$ s later. What is the depth of the seabed, expressed in standard scientific notation?

   • A) $3.6 \times 10^1$ m
   • B) $7.2 \times 10^1$ m
   • C) $3.6 \times 10^2$ m
   • D) $7.2 \times 10^2$ m
2. 2.

   During a high-speed aerodynamic braking test, a prototype projectile decelerates uniformly from an initial speed of $5.4 \times 10^2$ m/s to a final speed of $6.0 \times 10^1$ m/s over a time interval of $1.6 \times 10^{-3}$ s. The magnitude of average acceleration is defined as $a = \frac{|\Delta v|}{\Delta t}$. What is the magnitude of the projectile's acceleration, expressed in standard scientific notation?

   • A) $3.0 \times 10^5$ m/s²
   • B) $3.0 \times 10^{-1}$ m/s²
   • C) $3.75 \times 10^5$ m/s²
   • D) $3.0 \times 10^4$ m/s²
3. 3.

   An electric heating element rated at $2.5 \times 10^1$ W runs continuously for $4.0 \times 10^2$ s to warm a metal test plate. The total thermal energy supplied is calculated using $E = P \times t$. If this energy is distributed uniformly across a plate area of $5.0 \times 10^{-3}$ m², what is the thermal energy received per unit area in J/m², expressed in standard scientific notation?

   • A) $2.0 \times 10^5$ J/m²
   • B) $2.0 \times 10^6$ J/m²
   • C) $5.0 \times 10^6$ J/m²
   • D) $2.0 \times 10^7$ J/m²
4. 4.

   During a thermal analysis experiment, a sample of liquid coolant with a mass of $5.0 \times 10^{-1}\text{ kg}$ and a specific heat capacity of $2.4 \times 10^3\text{ J/(kg}\cdot^\circ\text{C)}$ is heated uniformly. The temperature of the coolant increases from $2.0 \times 10^1\ ^\circ\text{C}$ to $6.5 \times 10^1\ ^\circ\text{C}$. Given that thermal energy absorbed is calculated using $Q = m c \Delta T$, what is the total energy transferred to the coolant expressed in standard scientific notation?

   • A) $5.4 \times 10^4\text{ J}$
   • B) $5.4 \times 10^3\text{ J}$
   • C) $7.8 \times 10^4\text{ J}$
   • D) $5.4 \times 10^5\text{ J}$
5. 5.

   During an aerospace safety study, researchers evaluate the impact hazard of orbital debris striking satellite shielding. A high-velocity debris particle with a mass of $4.0 \times 10^{-5}\text{ kg}$ travels at a speed of $8.0 \times 10^3\text{ m/s}$. Given that kinetic energy is calculated as $E_k = \frac{1}{2}mv^2$, what is the kinetic energy of the particle expressed in standard scientific notation?

   • A) $1.28 \times 10^2\text{ J}$
   • B) $1.28 \times 10^3\text{ J}$
   • C) $2.56 \times 10^3\text{ J}$
   • D) $1.6 \times 10^{-1}\text{ J}$
6. 6.

   During an electrostatics investigation, a constant electric current of $3.2 \times 10^{-3}\text{ A}$ flows through a circuit for $2.5 \times 10^2\text{ s}$. The total electric charge transferred is given by $Q = I \times t$, and each elementary charge has a magnitude of $1.6 \times 10^{-19}\text{ C}$. How many electrons pass through the circuit during this time, expressed in standard scientific notation?

   • A) $5.0 \times 10^{17}$
   • B) $5.0 \times 10^{18}$
   • C) $5.0 \times 10^{-20}$
   • D) $2.0 \times 10^{18}$
7. 7.

   In a materials testing laboratory, a micro-actuator applies a normal force of $3.6 \times 10^{-3}\text{ N}$ onto a flat sensor surface with an area of $8.0 \times 10^{-8}\text{ m}^2$. Pressure is defined as the force applied per unit area ($P = \frac{F}{A}$). What is the pressure exerted on the sensor, expressed in standard scientific notation in pascals ($\text{Pa}$)?

   • A) $2.88 \times 10^{-10}\text{ Pa}$
   • B) $4.5 \times 10^5\text{ Pa}$
   • C) $4.5 \times 10^4\text{ Pa}$
   • D) $4.5 \times 10^{-12}\text{ Pa}$
8. 8.

   During a semiconductor fabrication process, a pure silicon wafer has a mass of $5.4 \times 10^{-2}\text{ kg}$. The average mass of a single silicon atom is $4.5 \times 10^{-26}\text{ kg}$. A precision laser etching procedure selectively removes a fraction of $5.0 \times 10^{-4}$ of the total atoms present in the wafer. How many silicon atoms are removed during this process, expressed in standard scientific notation?

   • A) $1.2 \times 10^{24}$
   • B) $6.0 \times 10^{19}$
   • C) $6.0 \times 10^{20}$
   • D) $2.4 \times 10^{27}$
9. 9.

   A solar irradiance detector with an active surface area of $4.0 \times 10^{-4}\text{ m}^2$ is tested under a uniform radiation beam providing an intensity of $6.5 \times 10^2\text{ W/m}^2$. If radiant energy strikes the detector continuously for $5.0 \times 10^2\text{ s}$, what is the total radiant energy received by the active area, expressed in standard scientific notation?

   • A) $1.3 \times 10^1\text{ J}$
   • B) $1.3 \times 10^2\text{ J}$
   • C) $1.3 \times 10^3\text{ J}$
   • D) $1.3 \times 10^{-1}\text{ J}$
10. 10.

    In a microfluidics experiment, a syringe pump delivers a solution at a constant volumetric flow rate of $4.5 \times 10^{-8}\text{ m}^3\text{/s}$ into a vertical cylindrical well with a flat base area of $1.5 \times 10^{-3}\text{ m}^2$. If the pump runs continuously for $2.0 \times 10^2\text{ s}$, what is the final liquid depth in the well, expressed in standard scientific notation in meters?

    • A) $6.0 \times 10^{-9}\text{ m}$
    • B) $3.0 \times 10^{-5}\text{ m}$
    • C) $6.0 \times 10^{-2}\text{ m}$
    • D) $6.0 \times 10^{-3}\text{ m}$
11. 11.

    In an atomic physics lesson, a student models an atom as a sphere with a radius of $1.5 \times 10^{-10}\text{ m}$ and its nucleus as a sphere with a radius of $3.0 \times 10^{-15}\text{ m}$. The student wants to determine how many times larger the volume of the atom is compared to the volume of the nucleus. Assuming both structures are spherical, what is the ratio of the atom's volume to the nucleus's volume expressed in standard scientific notation?

    • A) $1.25 \times 10^{14}$
    • B) $1.25 \times 10^{15}$
    • C) $2.50 \times 10^9$
    • D) $5.00 \times 10^4$
12. 12.

    A laboratory centrifuge collects suspended micro-particles from liquid samples during an environmental physics study. In a single run, the centrifuge isolates $4.0 \times 10^5$ identical particles, each having a mass of 0.075 mg. What is the total mass of the collected particles expressed in standard scientific notation in kilograms (kg)?

    • A) $3.0 \times 10^{-4}$ kg
    • B) $3.0 \times 10^{-1}$ kg
    • C) $3.0 \times 10^{-2}$ kg
    • D) $3.0 \times 10^1$ kg