Unit conversion with ratios Transitional Reasoning Practice

Questions

1. 1.

   During a static test firing, an aerospace rocket engine consumes liquid propellant at a steady mass flow rate of 360 kilograms per minute (kg/min). To calibrate high-frequency digital telemetry sensors that measure propellant flow in grams per millisecond (g/ms), a propulsion technician must convert this rate using unit conversion ratios. Given that 1 kilogram equals 1,000 grams, 1 minute equals 60 seconds, and 1 second equals 1,000 milliseconds, what is this propellant mass flow rate expressed in grams per millisecond?

   • A) 6 g/ms
   • B) 60 g/ms
   • C) 6,000 g/ms
   • D) 0.006 g/ms
2. 2.

   A geotechnical engineer evaluates the foundation soil for a commercial building and determines that the ground has an allowable bearing capacity of 350 kilonewtons per square meter (kN/m²). To calibrate an on-site electronic testing probe whose digital sensor registers force per unit area in newtons per square centimeter (N/cm²), the engineer needs to convert this capacity using unit conversion ratios. Given that 1 kilonewton equals 1,000 newtons and 1 square meter equals 10,000 square centimeters, what is this bearing capacity expressed in newtons per square centimeter?

   • A) 3.5 N/cm²
   • B) 35 N/cm²
   • C) 350 N/cm²
   • D) 3,500 N/cm²
3. 3.

   An electric delivery van consumes electrical energy at an average rate of 240 watt-hours per kilometer (Wh/km). To input this parameter into a traction simulation that requires standard base units, an automotive engineer converts the consumption rate into joules per meter (J/m) using unit conversion ratios. Given that 1 watt-hour equals 3,600 joules and 1 kilometer equals 1,000 meters, what is the van's energy consumption expressed in joules per meter?

   • A) 14.4 J/m
   • B) 66.7 J/m
   • C) 240 J/m
   • D) 864 J/m
4. 4.

   In an automated genetics laboratory, a micro-infusion pump dispenses liquid reagent into an assay plate at a constant rate of 125 microliters per minute (μL/min). To program the primary reservoir software for continuous multi-day operations, a laboratory technician needs to express this dispensing rate in milliliters per day (mL/day). Using unit conversion ratios, what is this dispensing rate expressed in milliliters per day?

   • A) 7.5 mL/day
   • B) 180 mL/day
   • C) 3.0 mL/day
   • D) 1,800 mL/day
5. 5.

   A coastal desalination facility produces fresh drinking water at a steady rate of 540 cubic meters per day ($\text{m}^3/\text{day}$). To monitor real-time output against municipal pipeline targets, an operations engineer must convert this production rate into liters per minute ($\text{L/min}$). Using unit conversion ratios, what is this water production rate expressed in liters per minute?

   • A) 375 L/min
   • B) 150 L/min
   • C) 37.5 L/min
   • D) 22,500 L/min
6. 6.

   A long-haul commercial truck consumes diesel exhaust fluid at an average rate of 1.8 liters per 100 kilometers traveled. While maintaining a steady cruising speed of 90 kilometers per hour on a highway, an automated injector continuously meters the fluid into the exhaust stream. Using unit conversion ratios, what is this fluid consumption rate expressed in milliliters per minute?

   • A) 16.2 mL/min
   • B) 27 mL/min
   • C) 97.2 mL/min
   • D) 2,700 mL/min
7. 7.

   An astronomical tracking station observes a near-Earth asteroid moving across a telescope field of view at a steady angular speed of 75 arcseconds per minute. To enter this trajectory into long-term orbital modeling software, an astronomer must convert the speed into degrees per day. Given that 1 degree equals 60 arcminutes, 1 arcminute equals 60 arcseconds, and 1 day equals 24 hours, what is this tracking speed expressed in degrees per day?

   • A) 30 degrees per day
   • B) 1.25 degrees per day
   • C) 72 degrees per day
   • D) 180 degrees per day
8. 8.

   An aerospace materials laboratory is evaluating a carbon-composite panel with a measured density of 1.6 grams per cubic centimeter ($\text{g/cm}^3$). To run structural load simulations that require standard metric units, an engineer must convert this measurement into kilograms per cubic meter ($\text{kg/m}^3$) using unit conversion ratios. Given that 1 kilogram equals 1,000 grams and 1 meter equals 100 centimeters, what is the density of the composite panel in kilograms per cubic meter?

   • A) $0.16\text{ kg/m}^3$
   • B) $1,600\text{ kg/m}^3$
   • C) $16\text{ kg/m}^3$
   • D) $1,600,000\text{ kg/m}^3$
9. 9.

   A solar energy research station records an incoming solar irradiance of 850 watts per square meter ($\text{W/m}^2$) on a photovoltaic test surface. To calibrate a miniature optical photodiode designed to monitor cell performance, an engineer must convert this irradiance into milliwatts per square centimeter ($\text{mW/cm}^2$) using unit conversion ratios. Using the conversion facts that 1 watt equals 1,000 milliwatts and 1 meter equals 100 centimeters, what is this solar irradiance in milliwatts per square centimeter?

   • A) 8.5 $\text{mW/cm}^2$
   • B) 85 $\text{mW/cm}^2$
   • C) 850 $\text{mW/cm}^2$
   • D) 8,500 $\text{mW/cm}^2$
10. 10.

    A pharmaceutical cleanroom ventilation system circulates air at a constant rate of 54 cubic meters per hour ($\text{m}^3/\text{h}$). To calibrate an optical particle counter, a technician must convert this volumetric flow rate into cubic centimeters per second ($\text{cm}^3/\text{s}$) using unit conversion ratios. Given that 1 meter equals 100 centimeters (so $1\text{ m}^3 = 1\,000\,000\text{ cm}^3$) and 1 hour equals 3,600 seconds, what is this flow rate in cubic centimeters per second?

    • A) $15\,000\text{ cm}^3/\text{s}$
    • B) $1\,500\text{ cm}^3/\text{s}$
    • C) $150\text{ cm}^3/\text{s}$
    • D) $1.5\text{ cm}^3/\text{s}$
11. 11.

    In a hospital clinic, an intravenous drip delivers medication at a steady rate of 15 drops per minute. The calibrated delivery tubing supplies 20 drops for every 1 milliliter of fluid. Using unit conversion ratios, what is this medication infusion rate expressed in liters per day (L/day)?

    • A) 432 L/day
    • B) 0.045 L/day
    • C) 10.8 L/day
    • D) 1.08 L/day
12. 12.

    An autonomous agricultural combine harvester clears a grain field at a steady pace of 1.8 hectares per hour. To calibrate the vehicle's real-time mapping system, an agronomist must express this work rate in square meters per minute using unit conversion ratios. Given that 1 hectare equals 10,000 square meters and 1 hour equals 60 minutes, what is the clearing rate in square meters per minute?

    • A) 30 square meters per minute
    • B) 108 square meters per minute
    • C) 300 square meters per minute
    • D) 1,800 square meters per minute
13. 13.

    A geological survey team operates a diamond core drill that penetrates bedrock at a steady rate of 18 centimeters per hour. To program the drill's micro-feed sensors, an engineer converts this penetration rate into micrometers per second using unit conversion ratios. Given that 1 centimeter equals 10,000 micrometers and 1 hour equals 3,600 seconds, what is this penetration rate in micrometers per second?

    • A) 5 micrometers per second
    • B) 20 micrometers per second
    • C) 50 micrometers per second
    • D) 500 micrometers per second
14. 14.

    An oceanographic research buoy transmits marine sensor data at a steady rate of 16 kilobits per second (kb/s). To plan daily data storage on an archive server in megabytes per day (MB/day), a network engineer applies the conversion ratios $1\text{ byte} = 8\text{ bits}$, $1\text{ megabyte} = 1\,000\text{ kilobytes}$, and $1\text{ day} = 86\,400\text{ seconds}$. Using unit conversion ratios, what is this data transmission rate expressed in megabytes per day?

    • A) 172.8 MB/day
    • B) 1,382.4 MB/day
    • C) 11,059.2 MB/day
    • D) 7.2 MB/day
15. 15.

    A commercial cargo ship operates with a steady fuel consumption rate of 43.2 metric tons per day (t/day). To calibrate the vessel's computerized engine-monitoring sensors, a marine engineer must convert this consumption rate into grams per second (g/s). Using unit conversion ratios, what is this fuel consumption rate in grams per second?

    • A) 500 g/s
    • B) 1,800 g/s
    • C) 50 g/s
    • D) 12,000 g/s
16. 16.

    An industrial mixing turbine operates at a steady speed of 450 revolutions per minute. To synchronize the mixer with an optical quality-control sensor, a plant technician must convert this rotational speed into degrees per second. Using unit conversion ratios, what is this rotational speed in degrees per second?

    • A) 2,700 degrees per second
    • B) 162,000 degrees per second
    • C) 75 degrees per second
    • D) 7.5 degrees per second
17. 17.

    A remote environmental monitoring station is powered by a micro-generator that produces electrical energy at an average rate of 250 joules per second (J/s). To evaluate the station's energy budget for daily battery storage, an electrical technician needs to convert this rate into megajoules per day (MJ/day). Using unit conversion ratios, what is this energy generation rate in megajoules per day?

    • A) 0.9 MJ/day
    • B) 21.6 MJ/day
    • C) 86.4 MJ/day
    • D) 216.0 MJ/day
18. 18.

    A logistics distribution center operates an automated parcel sorting line that moves at a constant speed of 1.25 meters per second. To synchronize the line with digital optical scanners calibrated in kilometers per hour, a systems technician needs to convert this speed using unit conversion ratios. What is the sorting line's speed expressed in kilometers per hour?

    • A) 0.45 km/h
    • B) 2.25 km/h
    • C) 4.5 km/h
    • D) 7.5 km/h
19. 19.

    An automated greenhouse irrigation line supplies water at a steady rate of 180 liters per hour. To set the timing for individual micro-drip nozzles, a technician needs to express this flow rate in milliliters per second. Using unit conversion ratios, what is this flow rate in milliliters per second?

    • A) 3,000 mL/s
    • B) 10.8 mL/s
    • C) 50 mL/s
    • D) 0.05 mL/s

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