8.18 Unit Conversions and Dimensional Analysis

Flashcards cover conversion factors, planning, metric-to-metric steps, density as a conversion factor, key unit conversions, significant figures, and example problems discussed in the lecture.

What is the starting unit and the desired end unit in dimensional analysis?

Starting unit is the unit you begin with; the desired end unit is the unit you must reach. Identify both before building your plan.

What is a conversion factor and how is it formed from an equality?

A conversion factor is a ratio formed from an equality that equals 1, written as either A/B or B/A, used to cancel units.

How do you turn any equality into a conversion factor?

Rewrite the equality as a ratio (e.g., A = B becomes A/B = 1 or B/A = 1) to multiply with quantities to convert units.

How should you plan a conversion problem?

First write a plan mapping the path from start to end units, then list the needed conversion factors before performing calculations.

What does 'per' indicate in a density or ratio statement?

It indicates a rate or ratio, such as mass per volume in density (g/cm^3).

What is the relationship between liters and cubic centimeters?

1 L = 1000 cm^3 and 1 cm^3 = 1 mL; used to convert L to cm^3 and vice versa.

What is the relationship between inches and centimeters when converting volumes?

1 in = 2.54 cm; for cubic conversions, cube both sides: 1 in^3 = 16.4 cm^3.

Convert 1.76 yards to centimeters (three significant figures).

1 yd = 91.44 cm; 1.76 yd × 91.44 cm/yd ≈ 161 cm (3 sig figs).

How do you handle cubic-unit conversions from inches to centimeters?

Cube the linear conversion: 1 in^3 = (2.54 cm)^3 ≈ 16.4 cm^3; so 1 cm^3 ≈ 0.0610 in^3.

What is the plan for converting 5.7 L to cm^3, and why is showing steps important?

Plan includes metric-to-metric steps: L to mL, then mL to cm^3; show every step to earn full points and ensure correct cancellations.

How many cubic centimeters is 5.7 liters?

5700 cm^3 (since 1 L = 1000 cm^3).

How do you convert 30 mL to quarts?

Convert mL to L (30 mL = 0.030 L) or use 1 qt ≈ 0.946353 L; 30 mL ≈ 0.0317 qt.

How is density used as a conversion factor?

Density is mass/volume. To convert between mass and volume, use density as the ratio to cancel units: mass = density × volume (with appropriate unit alignment).

What is the mass in kilograms of 1.73×10^5 L of jet fuel with density 176 g/L?

Mass = volume × density = 1.73×10^5 L × 176 g/L = 3.0448×10^7 g = 3.0448×10^4 kg (3.04×10^4 kg) with 3 sig figs.

How many calories are burned in a 26.2 mile race given pace 13.1 miles/hour and 665 calories/hour?

Time = distance/speed = 26.2/13.1 ≈ 2.0 h; energy = rate × time = 665 × 2 ≈ 1330 cal = 1.33×10^3 cal.

Why is it important to show every step in dimensional analysis?

Many rubrics award points for correct setup and unit cancellations; skipping steps can lose points even if the final answer is correct.

What are “quality statements” and how are they used?

Quality statements express unit relationships (e.g., yards to meters) and can be manipulated to create useful conversion factors while maintaining equality.

What is the impact of exact numbers on significant figures?

Exact numbers have unlimited significant figures and do not limit the precision of the final result (e.g., defined unit conversions).