Unit conversion — Digital SAT Math practice
Chain conversion factors and track units.
Key terms
- Conversion Factor: A ratio equal to one that relates two different units of the same measurement.
- Dimensional Analysis: Method of solving problems by tracking units through multiplication and cancellation.
- Linear Scale Factor: Ratio comparing lengths between two similar figures or unit systems.
- Compound Unit: A measurement expressed as a ratio of two different quantities, like miles per hour.
- Cubic Conversion: Scaling volume by the cube of the linear conversion factor between units.
Common traps
- Forgetting to square or cube the conversion factor when working with area or volume units.
- Flipping the conversion fraction so unwanted units multiply instead of canceling out.
- Converting only the numerator or denominator in a rate without adjusting both units.
- Assuming linear conversion factors apply directly to squared or cubed measurements.
Key ideas to know
Chain Conversion Factors
Convert 2.5 hours into seconds using chain conversion factors. Show each step with units canceling out.
Multiply by fractions equal to 1 so unwanted units cancel. Use (60 min / 1 hr) and (60 sec / 1 min). Units cancel left to right, leaving only seconds.
Watch out: Writing conversion factors upside down so the unwanted unit multiplies instead of canceling.
Area and Volume Scaling
If 1 yard equals 3 feet, what is the conversion factor to change square yards to square feet?
Square the linear factor. Since 1 yd = 3 ft, multiply by (3 ft / 1 yd)2 or use 9 ft2 / 1 yd2.
Watch out: Using the linear factor directly for area or volume instead of squaring or cubing it.
Rate Conversion Pitfall
A student converts 60 miles per hour to feet per second by calculating 60 × 3600 / 5280. Identify the error in this setup and provide the correct calculation.
The student canceled units incorrectly. To cancel miles, multiply by (5280 ft / 1 mi). To cancel hours, multiply by (1 hr / 3600 sec). Correct: 60 × 5280 / 3600 = 88 ft/sec.
Watch out: Flipping the time conversion factor so hours multiply instead of canceling, or dividing by the factor.
Sample questions
Question 1
A car travels 180 kilometers in 2 hours. What is its average speed in meters per second?
- 50 m/s
- 25 m/s
- 90 m/s
- 2.5 m/s
Show answer and explanation
Answer: 25 m/s
90 km/h = 90,000 m / 3600 s = 25 m/s.